diff --git a/clang-tools-extra/clangd/Threading.cpp b/clang-tools-extra/clangd/Threading.cpp
--- a/clang-tools-extra/clangd/Threading.cpp
+++ b/clang-tools-extra/clangd/Threading.cpp
@@ -1,5 +1,6 @@
 #include "Threading.h"
 #include "Trace.h"
+#include "clang/Basic/Stack.h"
 #include "llvm/ADT/ScopeExit.h"
 #include "llvm/Support/FormatVariadic.h"
 #include "llvm/Support/Threading.h"
@@ -86,16 +87,16 @@
     }
   });
 
-  std::thread(
-      [](std::string Name, decltype(Action) Action, decltype(CleanupTask)) {
-        llvm::set_thread_name(Name);
-        Action();
-        // Make sure function stored by Action is destroyed before CleanupTask
-        // is run.
-        Action = nullptr;
-      },
-      Name.str(), std::move(Action), std::move(CleanupTask))
-      .detach();
+  auto Task = [Name = Name.str(), Action = std::move(Action),
+               Cleanup = std::move(CleanupTask)]() mutable {
+    llvm::set_thread_name(Name);
+    Action();
+    // Make sure function stored by ThreadFunc is destroyed before Cleanup runs.
+    Action = nullptr;
+  };
+
+  // Ensure our worker threads have big enough stacks to run clang.
+  llvm::llvm_execute_on_thread_async(std::move(Task), clang::DesiredStackSize);
 }
 
 Deadline timeoutSeconds(llvm::Optional<double> Seconds) {
diff --git a/clang-tools-extra/clangd/unittests/ClangdTests.cpp b/clang-tools-extra/clangd/unittests/ClangdTests.cpp
--- a/clang-tools-extra/clangd/unittests/ClangdTests.cpp
+++ b/clang-tools-extra/clangd/unittests/ClangdTests.cpp
@@ -1065,6 +1065,27 @@
                                 Field(&CodeCompletion::Scope, "ns::"))));
 }
 
+TEST_F(ClangdVFSTest, TestStackOverflow) {
+  MockFSProvider FS;
+  ErrorCheckingCallbacks DiagConsumer;
+  MockCompilationDatabase CDB;
+  ClangdServer Server(CDB, FS, ClangdServer::optsForTest(), &DiagConsumer);
+
+  const char *SourceContents = R"cpp(
+    constexpr int foo() { return foo(); }
+    static_assert(foo());
+  )cpp";
+
+  auto FooCpp = testPath("foo.cpp");
+  FS.Files[FooCpp] = SourceContents;
+
+  Server.addDocument(FooCpp, SourceContents);
+  ASSERT_TRUE(Server.blockUntilIdleForTest()) << "Waiting for diagnostics";
+  // check that we got a constexpr depth error, and not crashed by stack
+  // overflow
+  EXPECT_TRUE(DiagConsumer.hadErrorInLastDiags());
+}
+
 } // namespace
 } // namespace clangd
 } // namespace clang