Index: lib/CodeGen/BackendUtil.cpp
===================================================================
--- lib/CodeGen/BackendUtil.cpp
+++ lib/CodeGen/BackendUtil.cpp
@@ -1155,15 +1155,14 @@
       continue;
 
     auto GUID = GlobalList.first;
-    assert(GlobalList.second.SummaryList.size() == 1 &&
-           "Expected individual combined index to have one summary per GUID");
-    auto &Summary = GlobalList.second.SummaryList[0];
-    // Skip the summaries for the importing module. These are included to
-    // e.g. record required linkage changes.
-    if (Summary->modulePath() == M->getModuleIdentifier())
-      continue;
-    // Add an entry to provoke importing by thinBackend.
-    ImportList[Summary->modulePath()].insert(GUID);
+    for (auto &Summary : GlobalList.second.SummaryList) {
+      // Skip the summaries for the importing module. These are included to
+      // e.g. record required linkage changes.
+      if (Summary->modulePath() == M->getModuleIdentifier())
+        continue;
+      // Add an entry to provoke importing by thinBackend.
+      ImportList[Summary->modulePath()].insert(GUID);
+    }
   }
 
   std::vector<std::unique_ptr<llvm::MemoryBuffer>> OwnedImports;
Index: test/CodeGen/Inputs/thinlto_backend_local_name_conflict1.ll
===================================================================
--- test/CodeGen/Inputs/thinlto_backend_local_name_conflict1.ll
+++ test/CodeGen/Inputs/thinlto_backend_local_name_conflict1.ll
@@ -0,0 +1,13 @@
+; ModuleID = 'local_name_conflict_var.o'
+source_filename = "local_name_conflict_var.c"
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+@baz = internal global i32 10, align 4
+
+; Function Attrs: noinline nounwind uwtable
+define i32 @a() {
+entry:
+  %0 = load i32, i32* @baz, align 4
+  ret i32 %0
+}
Index: test/CodeGen/Inputs/thinlto_backend_local_name_conflict2.ll
===================================================================
--- test/CodeGen/Inputs/thinlto_backend_local_name_conflict2.ll
+++ test/CodeGen/Inputs/thinlto_backend_local_name_conflict2.ll
@@ -0,0 +1,13 @@
+; ModuleID = 'local_name_conflict_var.o'
+source_filename = "local_name_conflict_var.c"
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+@baz = internal global i32 10, align 4
+
+; Function Attrs: noinline nounwind uwtable
+define i32 @b() {
+entry:
+  %0 = load i32, i32* @baz, align 4
+  ret i32 %0
+}
Index: test/CodeGen/thinlto_backend_local_name_conflict.ll
===================================================================
--- test/CodeGen/thinlto_backend_local_name_conflict.ll
+++ test/CodeGen/thinlto_backend_local_name_conflict.ll
@@ -0,0 +1,34 @@
+; Test handling when two files with the same source file name contain
+; static read only variables with the same name (which will have the same GUID
+; in the combined index).
+
+; Do setup work for all below tests: generate bitcode and combined index
+; RUN: opt -module-summary -module-hash %s -o %t.bc
+; RUN: opt -module-summary -module-hash %p/Inputs/thinlto_backend_local_name_conflict1.ll -o %t2.bc
+; RUN: opt -module-summary -module-hash %p/Inputs/thinlto_backend_local_name_conflict2.ll -o %t3.bc
+; RUN: llvm-lto -thinlto-action=thinlink -o %t4.bc %t.bc %t2.bc %t3.bc
+; RUN: llvm-lto -thinlto-action=distributedindexes -exported-symbol=main -thinlto-index=%t4.bc %t.bc
+
+; This module will import a() and b() which should cause the read only copy
+; of baz from each of those modules to be imported. Check that the both are
+; imported as local copies.
+; RUN: %clang -target x86_64-unknown-linux-gnu -O2 -o %t4.o -x ir %t.bc -c -fthinlto-index=%t.bc.thinlto.bc -save-temps=obj
+; RUN: llvm-dis %t.s.3.import.bc -o - | FileCheck --check-prefix=IMPORT %s
+; IMPORT: @baz.llvm.{{.*}} = internal global i32 10
+; IMPORT: @baz.llvm.{{.*}} = internal global i32 10
+
+; ModuleID = 'local_name_conflict_var_main.o'
+source_filename = "local_name_conflict_var_main.c"
+target datalayout = "e-m:e-i64:64-f80:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+; Function Attrs: noinline nounwind uwtable
+define i32 @main() {
+entry:
+  %call1 = call i32 (...) @a()
+  %call2 = call i32 (...) @b()
+  ret i32 0
+}
+
+declare i32 @a(...)
+declare i32 @b(...)