Index: clang/include/clang/Lex/ModuleMap.h
===================================================================
--- clang/include/clang/Lex/ModuleMap.h
+++ clang/include/clang/Lex/ModuleMap.h
@@ -413,6 +413,7 @@
 
   /// Is this a compiler builtin header?
   static bool isBuiltinHeader(StringRef FileName);
+  bool isBuiltinHeader(const FileEntry *File);
 
   /// Add a module map callback.
   void addModuleMapCallbacks(std::unique_ptr<ModuleMapCallbacks> Callback) {
Index: clang/lib/Lex/HeaderSearch.cpp
===================================================================
--- clang/lib/Lex/HeaderSearch.cpp
+++ clang/lib/Lex/HeaderSearch.cpp
@@ -1276,14 +1276,12 @@
     //
     // It's common that libc++ and system modules will both define such
     // submodules. Make sure cached results for a builtin header won't
-    // prevent other builtin modules to potentially enter the builtin header.
-    // Note that builtins are header guarded and the decision to actually
-    // enter them is postponed to the controlling macros logic below.
+    // prevent other builtin modules from potentially entering the builtin
+    // header. Note that builtins are header guarded and the decision to
+    // actually enter them is postponed to the controlling macros logic below.
     bool TryEnterHdr = false;
     if (FileInfo.isCompilingModuleHeader && FileInfo.isModuleHeader)
-      TryEnterHdr = File->getDir() == ModMap.getBuiltinDir() &&
-                    ModuleMap::isBuiltinHeader(
-                        llvm::sys::path::filename(File->getName()));
+      TryEnterHdr = ModMap.isBuiltinHeader(File);
 
     // Textual headers can be #imported from different modules. Since ObjC
     // headers find in the wild might rely only on #import and do not contain
@@ -1416,20 +1414,31 @@
                           ModuleMap::KnownHeader *SuggestedModule) {
   ModuleMap::KnownHeader Module =
       HS.findModuleForHeader(File, /*AllowTextual*/true);
-  if (SuggestedModule)
-    *SuggestedModule = (Module.getRole() & ModuleMap::TextualHeader)
-                           ? ModuleMap::KnownHeader()
-                           : Module;
 
   // If this module specifies [no_undeclared_includes], we cannot find any
   // file that's in a non-dependency module.
   if (RequestingModule && Module && RequestingModule->NoUndeclaredIncludes) {
-    HS.getModuleMap().resolveUses(RequestingModule, /*Complain*/false);
+    HS.getModuleMap().resolveUses(RequestingModule, /*Complain*/ false);
     if (!RequestingModule->directlyUses(Module.getModule())) {
+      // Builtin headers are a special case. Multiple modules can use the same
+      // builtin as a modular header (see also comment in
+      // ShouldEnterIncludeFile()), so the builtin header may have been
+      // "claimed" by an unrelated module. This shouldn't prevent us from
+      // including the builtin header textually in this module.
+      if (HS.getModuleMap().isBuiltinHeader(File)) {
+        if (SuggestedModule)
+          *SuggestedModule = ModuleMap::KnownHeader();
+        return true;
+      }
       return false;
     }
   }
 
+  if (SuggestedModule)
+    *SuggestedModule = (Module.getRole() & ModuleMap::TextualHeader)
+                           ? ModuleMap::KnownHeader()
+                           : Module;
+
   return true;
 }
 
Index: clang/lib/Lex/ModuleMap.cpp
===================================================================
--- clang/lib/Lex/ModuleMap.cpp
+++ clang/lib/Lex/ModuleMap.cpp
@@ -387,13 +387,17 @@
            .Default(false);
 }
 
+bool ModuleMap::isBuiltinHeader(const FileEntry *File) {
+  return File->getDir() == BuiltinIncludeDir &&
+         ModuleMap::isBuiltinHeader(llvm::sys::path::filename(File->getName()));
+}
+
 ModuleMap::HeadersMap::iterator
 ModuleMap::findKnownHeader(const FileEntry *File) {
   resolveHeaderDirectives(File);
   HeadersMap::iterator Known = Headers.find(File);
   if (HeaderInfo.getHeaderSearchOpts().ImplicitModuleMaps &&
-      Known == Headers.end() && File->getDir() == BuiltinIncludeDir &&
-      ModuleMap::isBuiltinHeader(llvm::sys::path::filename(File->getName()))) {
+      Known == Headers.end() && ModuleMap::isBuiltinHeader(File)) {
     HeaderInfo.loadTopLevelSystemModules();
     return Headers.find(File);
   }
Index: clang/test/Modules/Inputs/no-undeclared-includes-builtins/glibc/module.modulemap
===================================================================
--- /dev/null
+++ clang/test/Modules/Inputs/no-undeclared-includes-builtins/glibc/module.modulemap
@@ -0,0 +1,5 @@
+module glibc [system] [no_undeclared_includes] {
+  // glibc relies on the builtin stddef.h, so it has no stddef.h of its own.
+  header "stdio.h"
+  export *
+}
Index: clang/test/Modules/Inputs/no-undeclared-includes-builtins/glibc/stdio.h
===================================================================
--- /dev/null
+++ clang/test/Modules/Inputs/no-undeclared-includes-builtins/glibc/stdio.h
@@ -0,0 +1 @@
+#include <stddef.h>
Index: clang/test/Modules/Inputs/no-undeclared-includes-builtins/libcxx/module.modulemap
===================================================================
--- /dev/null
+++ clang/test/Modules/Inputs/no-undeclared-includes-builtins/libcxx/module.modulemap
@@ -0,0 +1,5 @@
+module libcxx [system] {
+  header "stddef.h"
+  header "stdio.h"
+  export *
+}
Index: clang/test/Modules/Inputs/no-undeclared-includes-builtins/libcxx/stddef.h
===================================================================
--- /dev/null
+++ clang/test/Modules/Inputs/no-undeclared-includes-builtins/libcxx/stddef.h
@@ -0,0 +1 @@
+#include_next <stddef.h>
Index: clang/test/Modules/Inputs/no-undeclared-includes-builtins/libcxx/stdio.h
===================================================================
--- /dev/null
+++ clang/test/Modules/Inputs/no-undeclared-includes-builtins/libcxx/stdio.h
@@ -0,0 +1 @@
+#include_next <stdio.h>
Index: clang/test/Modules/no-undeclared-includes-builtins.cpp
===================================================================
--- /dev/null
+++ clang/test/Modules/no-undeclared-includes-builtins.cpp
@@ -0,0 +1,14 @@
+// Test that a [no_undeclared_headers] module can include builtin headers, even
+// if these have been "claimed" by a different module that wraps these builtin
+// headers. libc++ does this, for example.
+//
+// The test inputs used here replicates the relationship between libc++ and
+// glibc. When modularizing glibc, [no_undeclared_headers] must be used to
+// prevent glibc from including the libc++ versions of the C standard library
+// headers.
+
+// RUN: rm -rf %t
+// RUN: %clang_cc1 -fmodules-cache-path=%t -fmodules -fimplicit-module-maps -I %S/Inputs/no-undeclared-includes-builtins/libcxx -I %S/Inputs/no-undeclared-includes-builtins/glibc %s
+// expected-no-diagnostics
+
+#include <stddef.h>