diff --git a/source/opt/ssa_rewrite_pass.cpp b/source/opt/ssa_rewrite_pass.cpp
index f2cb2da28..7144ca0ca 100644
--- a/source/opt/ssa_rewrite_pass.cpp
+++ b/source/opt/ssa_rewrite_pass.cpp
@@ -102,6 +102,7 @@ void SSARewriter::ReplacePhiUsersWith(const PhiCandidate& phi_to_remove,
                                       uint32_t repl_id) {
   for (uint32_t user_id : phi_to_remove.users()) {
     PhiCandidate* user_phi = GetPhiCandidate(user_id);
+    BasicBlock* bb = pass_->context()->get_instr_block(user_id);
     if (user_phi) {
       // If the user is a Phi candidate, replace all arguments that refer to
       // |phi_to_remove.result_id()| with |repl_id|.
@@ -110,6 +111,10 @@ void SSARewriter::ReplacePhiUsersWith(const PhiCandidate& phi_to_remove,
           arg = repl_id;
         }
       }
+    } else if (bb->id() == user_id) {
+      // The phi candidate is the definition of the variable at basic block
+      // |bb|.  We must change this to the replacement.
+      WriteVariable(phi_to_remove.var_id(), bb, repl_id);
     } else {
       // For regular loads, traverse the |load_replacement_| table looking for
       // instances of |phi_to_remove|.
@@ -259,6 +264,8 @@ uint32_t SSARewriter::GetReachingDef(uint32_t var_id, BasicBlock* bb) {
     // require a Phi instruction.  This will act as |var_id|'s current
     // definition to break potential cycles.
     PhiCandidate& phi_candidate = CreatePhiCandidate(var_id, bb);
+
+    // Set the value for |bb| to avoid an infinite recursion.
     WriteVariable(var_id, bb, phi_candidate.result_id());
     val_id = AddPhiOperands(&phi_candidate);
   }
diff --git a/source/opt/ssa_rewrite_pass.h b/source/opt/ssa_rewrite_pass.h
index c0373dc06..fddbdaf54 100644
--- a/source/opt/ssa_rewrite_pass.h
+++ b/source/opt/ssa_rewrite_pass.h
@@ -188,6 +188,9 @@ class SSARewriter {
   // value |val_id|.
   void WriteVariable(uint32_t var_id, BasicBlock* bb, uint32_t val_id) {
     defs_at_block_[bb][var_id] = val_id;
+    if (auto* pc = GetPhiCandidate(val_id)) {
+      pc->AddUser(bb->id());
+    }
   }
 
   // Processes the store operation |inst| in basic block |bb|. This extracts
diff --git a/test/opt/local_ssa_elim_test.cpp b/test/opt/local_ssa_elim_test.cpp
index d2da1f9c1..a490d5290 100644
--- a/test/opt/local_ssa_elim_test.cpp
+++ b/test/opt/local_ssa_elim_test.cpp
@@ -1930,6 +1930,63 @@ TEST_F(LocalSSAElimTest, VariablePointerTest2) {
   SinglePassRunAndMatch<LocalMultiStoreElimPass>(text, false);
 }
 
+TEST_F(LocalSSAElimTest, ChainedTrivialPhis) {
+  // Check that the copy object get the undef value implicitly assigned in the
+  // entry block.
+  const std::string text = R"(
+; CHECK: [[undef:%\w+]] = OpUndef %v4float
+; CHECK: OpCopyObject %v4float [[undef]]
+               OpCapability Shader
+          %1 = OpExtInstImport "GLSL.std.450"
+               OpMemoryModel Logical GLSL450
+               OpEntryPoint GLCompute %2 "main"
+               OpExecutionMode %2 LocalSize 1 18 6
+               OpSource ESSL 310
+       %void = OpTypeVoid
+          %4 = OpTypeFunction %void
+       %bool = OpTypeBool
+      %float = OpTypeFloat 32
+    %v4float = OpTypeVector %float 4
+%_ptr_Function_v4float = OpTypePointer Function %v4float
+          %2 = OpFunction %void None %4
+          %9 = OpLabel
+         %10 = OpVariable %_ptr_Function_v4float Function
+               OpBranch %11
+         %11 = OpLabel
+               OpLoopMerge %12 %13 None
+               OpBranch %14
+         %14 = OpLabel
+         %15 = OpUndef %bool
+               OpBranchConditional %15 %16 %12
+         %16 = OpLabel
+         %17 = OpUndef %bool
+               OpSelectionMerge %18 None
+               OpBranchConditional %17 %19 %18
+         %19 = OpLabel
+         %20 = OpUndef %bool
+               OpLoopMerge %21 %22 None
+               OpBranchConditional %20 %23 %21
+         %23 = OpLabel
+         %24 = OpLoad %v4float %10
+         %25 = OpCopyObject %v4float %24
+         %26 = OpUndef %bool
+               OpBranch %22
+         %22 = OpLabel
+               OpBranch %19
+         %21 = OpLabel
+               OpBranch %12
+         %18 = OpLabel
+               OpBranch %13
+         %13 = OpLabel
+               OpBranch %11
+         %12 = OpLabel
+         %27 = OpLoad %v4float %10
+               OpReturn
+               OpFunctionEnd
+  )";
+  SinglePassRunAndMatch<SSARewritePass>(text, false);
+}
+
 // TODO(greg-lunarg): Add tests to verify handling of these cases:
 //
 //    No optimization in the presence of