diff --git a/csu/libc-tls.c b/csu/libc-tls.c
index bef92a7568..7d311056bc 100644
--- a/csu/libc-tls.c
+++ b/csu/libc-tls.c
@@ -145,11 +145,16 @@ __libc_setup_tls (void)
      _dl_allocate_tls_storage (in elf/dl-tls.c) does using __libc_memalign
      and dl_tls_static_align.  */
   tcb_offset = roundup (memsz + GLRO(dl_tls_static_surplus), max_align);
-  tlsblock = __sbrk (tcb_offset + TLS_INIT_TCB_SIZE + max_align);
+  tlsblock = _dl_early_allocate (tcb_offset + TLS_INIT_TCB_SIZE + max_align);
+  if (tlsblock == NULL)
+    _startup_fatal ("Fatal glibc error: Cannot allocate TLS block\n");
 #elif TLS_DTV_AT_TP
   tcb_offset = roundup (TLS_INIT_TCB_SIZE, align ?: 1);
-  tlsblock = __sbrk (tcb_offset + memsz + max_align
-		     + TLS_PRE_TCB_SIZE + GLRO(dl_tls_static_surplus));
+  tlsblock = _dl_early_allocate (tcb_offset + memsz + max_align
+				 + TLS_PRE_TCB_SIZE
+				 + GLRO(dl_tls_static_surplus));
+  if (tlsblock == NULL)
+    _startup_fatal ("Fatal glibc error: Cannot allocate TLS block\n");
   tlsblock += TLS_PRE_TCB_SIZE;
 #else
   /* In case a model with a different layout for the TCB and DTV
@@ -157,6 +162,7 @@ __libc_setup_tls (void)
 # error "Either TLS_TCB_AT_TP or TLS_DTV_AT_TP must be defined"
 #endif
 
+
   /* Align the TLS block.  */
   tlsblock = (void *) (((uintptr_t) tlsblock + max_align - 1)
 		       & ~(max_align - 1));
diff --git a/elf/Makefile b/elf/Makefile
index fc9860edee..ce3345ed92 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -33,6 +33,7 @@ routines = \
   $(all-dl-routines) \
   dl-addr \
   dl-addr-obj \
+  dl-early_allocate \
   dl-error \
   dl-iteratephdr \
   dl-libc \
@@ -108,6 +109,7 @@ all-dl-routines = $(dl-routines) $(sysdep-dl-routines)
 # But they are absent from the shared libc, because that code is in ld.so.
 elide-routines.os = \
   $(all-dl-routines) \
+  dl-early_allocate \
   dl-exception \
   dl-origin \
   dl-reloc-static-pie \
@@ -276,6 +278,7 @@ tests-static-normal := \
   tst-linkall-static \
   tst-single_threaded-pthread-static \
   tst-single_threaded-static \
+  tst-tls-allocation-failure-static \
   tst-tlsalign-extern-static \
   tst-tlsalign-static \
   # tests-static-normal
@@ -1213,6 +1216,10 @@ $(objpfx)tst-glibcelf.out: tst-glibcelf.py elf.h $(..)/scripts/glibcelf.py \
           --cc="$(CC) $(patsubst -DMODULE_NAME=%,-DMODULE_NAME=testsuite,$(CPPFLAGS))" \
 	  < /dev/null > $@ 2>&1; $(evaluate-test)
 
+ifeq ($(run-built-tests),yes)
+tests-special += $(objpfx)tst-tls-allocation-failure-static-patched.out
+endif
+
 # The test requires shared _and_ PIE because the executable
 # unit test driver must be able to link with the shared object
 # that is going to eventually go into an installed DSO.
@@ -2937,3 +2944,15 @@ $(eval $(call tst-trace-skeleton,4,\
 	$(objpfx)libtracemod2:$(objpfx)libtracemod3:$(objpfx)libtracemod4))
 $(eval $(call tst-trace-skeleton,5,\
 	$(objpfx)libtracemod2:$(objpfx)libtracemod3:$(objpfx)libtracemod4:$(objpfx)libtracemod5))
+
+$(objpfx)tst-tls-allocation-failure-static-patched: \
+  $(objpfx)tst-tls-allocation-failure-static $(..)scripts/tst-elf-edit.py
+	cp $< $@
+	$(PYTHON) $(..)scripts/tst-elf-edit.py --maximize-tls-size $@
+
+$(objpfx)tst-tls-allocation-failure-static-patched.out: \
+  $(objpfx)tst-tls-allocation-failure-static-patched
+	$< > $@ 2>&1; echo "status: $$?" >> $@
+	grep -q '^Fatal glibc error: Cannot allocate TLS block$$' $@ \
+	  && grep -q '^status: 127$$' $@; \
+	  $(evaluate-test)
diff --git a/elf/dl-early_allocate.c b/elf/dl-early_allocate.c
new file mode 100644
index 0000000000..d7f59d41e5
--- /dev/null
+++ b/elf/dl-early_allocate.c
@@ -0,0 +1,30 @@
+/* Early memory allocation for the dynamic loader.  Generic version.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <ldsodefs.h>
+#include <stddef.h>
+#include <unistd.h>
+
+void *
+_dl_early_allocate (size_t size)
+{
+  void *result = __sbrk (size);
+  if (result == (void *) -1)
+    _dl_fatal_printf ("Fatal glibc error: Early memory allocation failed\n");
+  return result;
+}
diff --git a/elf/tst-tls-allocation-failure-static.c b/elf/tst-tls-allocation-failure-static.c
new file mode 100644
index 0000000000..8de831b246
--- /dev/null
+++ b/elf/tst-tls-allocation-failure-static.c
@@ -0,0 +1,31 @@
+/* Base for test program with impossiblyh large PT_TLS segment.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+/* The test actual binary is patched using scripts/tst-elf-edit.py
+   --maximize-tls-size, and this introduces the expected test
+   allocation failure due to an excessive PT_LS p_memsz value.
+
+   Patching the binary is required because on some 64-bit targets, TLS
+   relocations can only cover a 32-bit range, and glibc-internal TLS
+   variables such as errno end up outside that range.  */
+
+int
+main (void)
+{
+  return 0;
+}
diff --git a/scripts/tst-elf-edit.py b/scripts/tst-elf-edit.py
index a514179bbf..0e19ce1e73 100644
--- a/scripts/tst-elf-edit.py
+++ b/scripts/tst-elf-edit.py
@@ -43,9 +43,11 @@ EI_DATA=5
 ELFDATA2LSB=b'\x01'
 ELFDATA2MSB=b'\x02'
 
+ET_EXEC=2
 ET_DYN=3
 
 PT_LOAD=1
+PT_TLS=7
 
 def elf_types_fmts(e_ident):
     endian = '<' if e_ident[EI_DATA] == ELFDATA2LSB else '>'
@@ -146,8 +148,15 @@ def elf_edit_align(phdr, align):
     else:
         phdr.p_align = int(align)
 
+def elf_edit_maximize_tls_size(phdr, elfclass):
+    if elfclass == ELFCLASS32:
+        # It is possible that the kernel can allocate half of the
+        # address space, so use something larger.
+        phdr.p_memsz = 0xfff00000
+    else:
+        phdr.p_memsz = 1 << 63
 
-def elf_edit(f, align):
+def elf_edit(f, opts):
     ei_nident_fmt = 'c' * EI_NIDENT
     ei_nident_len = struct.calcsize(ei_nident_fmt)
 
@@ -172,24 +181,35 @@ def elf_edit(f, align):
 
     ehdr = Elf_Ehdr(e_ident)
     ehdr.read(f)
-    if ehdr.e_type != ET_DYN:
-       error('{}: not a shared library'.format(f.name))
+    if ehdr.e_type not in (ET_EXEC, ET_DYN):
+       error('{}: not an executable or shared library'.format(f.name))
 
     phdr = Elf_Phdr(e_ident)
+    maximize_tls_size_done = False
     for i in range(0, ehdr.e_phnum):
         f.seek(ehdr.e_phoff + i * phdr.len)
         phdr.read(f)
-        if phdr.p_type == PT_LOAD:
-            elf_edit_align(phdr, align)
+        if phdr.p_type == PT_LOAD and opts.align is not None:
+            elf_edit_align(phdr, opts.align)
+            f.seek(ehdr.e_phoff + i * phdr.len)
+            phdr.write(f)
+            break
+        if phdr.p_type == PT_TLS and opts.maximize_tls_size:
+            elf_edit_maximize_tls_size(phdr, e_ident[EI_CLASS])
             f.seek(ehdr.e_phoff + i * phdr.len)
             phdr.write(f)
+            maximize_tls_size_done = True
             break
 
+    if opts.maximize_tls_size and not maximize_tls_size_done:
+        error('{}: TLS maximum size was not updated'.format(f.name))
 
 def get_parser():
     parser = argparse.ArgumentParser(description=__doc__)
-    parser.add_argument('-a', dest='align', required=True,
+    parser.add_argument('-a', dest='align',
                         help='How to set the LOAD alignment')
+    parser.add_argument('--maximize-tls-size', action='store_true',
+                        help='Set maximum PT_TLS size')
     parser.add_argument('output',
                         help='ELF file to edit')
     return parser
@@ -199,7 +219,7 @@ def main(argv):
     parser = get_parser()
     opts = parser.parse_args(argv)
     with open(opts.output, 'r+b') as fout:
-       elf_edit(fout, opts.align)
+       elf_edit(fout, opts)
 
 
 if __name__ == '__main__':
diff --git a/sysdeps/generic/ldsodefs.h b/sysdeps/generic/ldsodefs.h
index 4a5e698db2..5d0369358d 100644
--- a/sysdeps/generic/ldsodefs.h
+++ b/sysdeps/generic/ldsodefs.h
@@ -1211,6 +1211,11 @@ extern struct link_map * _dl_get_dl_main_map (void)
 # endif
 #endif
 
+/* Perform early memory allocation, avoding a TCB dependency.
+   Terminate the process if allocation fails.  May attempt to use
+   brk.  */
+void *_dl_early_allocate (size_t size) attribute_hidden;
+
 /* Initialize the DSO sort algorithm to use.  */
 #if !HAVE_TUNABLES
 static inline void
diff --git a/sysdeps/unix/sysv/linux/dl-early_allocate.c b/sysdeps/unix/sysv/linux/dl-early_allocate.c
new file mode 100644
index 0000000000..2c77b6e3ff
--- /dev/null
+++ b/sysdeps/unix/sysv/linux/dl-early_allocate.c
@@ -0,0 +1,81 @@
+/* Early memory allocation for the dynamic loader.  Generic version.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+/* Mark symbols hidden in static PIE for early self relocation to work.  */
+#if BUILD_PIE_DEFAULT
+# pragma GCC visibility push(hidden)
+#endif
+#include <startup.h>
+
+#include <ldsodefs.h>
+#include <stddef.h>
+#include <string.h>
+#include <sysdep.h>
+#include <unistd.h>
+
+#include <mmap_call.h>
+
+/* Defined in brk.c.  */
+extern void *__curbrk;
+
+void *
+_dl_early_allocate (size_t size)
+{
+  void *result;
+
+  if (__curbrk != NULL)
+    /* If the break has been initialized, brk must have run before,
+       so just call it once more.  */
+    {
+      result = __sbrk (size);
+      if (result == (void *) -1)
+        result = NULL;
+    }
+  else
+    {
+      /* If brk has not been invoked, there is no need to update
+         __curbrk.  The first call to brk will take care of that.  */
+      void *previous = (void *) INTERNAL_SYSCALL_CALL (brk, 0);
+      result = (void *) INTERNAL_SYSCALL_CALL (brk, previous + size);
+      if (result == previous)
+        result = NULL;
+      else
+        result = previous;
+    }
+
+  /* If brk fails, fall back to mmap.  This can happen due to
+     unfortunate ASLR layout decisions and kernel bugs, particularly
+     for static PIE.  */
+  if (result == NULL)
+    {
+      long int ret;
+      int prot = PROT_READ | PROT_WRITE;
+      int flags = MAP_PRIVATE | MAP_ANONYMOUS;
+#ifdef __NR_mmap2
+      ret = MMAP_CALL_INTERNAL (mmap2, 0, size, prot, flags, -1, 0);
+#else
+      ret = MMAP_CALL_INTERNAL (mmap, 0, size, prot, flags, -1, 0);
+#endif
+      if (INTERNAL_SYSCALL_ERROR_P (ret))
+        result = NULL;
+      else
+        result = (void *) ret;
+    }
+
+  return result;
+}
