Index: clang-tools-extra/trunk/clangd/Protocol.cpp
===================================================================
--- clang-tools-extra/trunk/clangd/Protocol.cpp
+++ clang-tools-extra/trunk/clangd/Protocol.cpp
@@ -25,6 +25,8 @@
   URI Result;
   Result.uri = uri;
   uri.consume_front("file://");
+  // Also trim authority-less URIs
+  uri.consume_front("file:");
   // For Windows paths e.g. /X:
   if (uri.size() > 2 && uri[0] == '/' && uri[2] == ':')
     uri.consume_front("/");
Index: clang-tools-extra/trunk/test/clangd/completion.test
===================================================================
--- clang-tools-extra/trunk/test/clangd/completion.test
+++ clang-tools-extra/trunk/test/clangd/completion.test
@@ -20,6 +20,16 @@
 # CHECK-DAG: {"label":"bb","kind":5}
 # CHECK-DAG: {"label":"ccc","kind":5}
 # CHECK: ]}
+Content-Length: 146
+
+{"jsonrpc":"2.0","id":1,"method":"textDocument/completion","params":{"textDocument":{"uri":"file:/main.cpp"},"position":{"line":3,"character":5}}}
+# Test authority-less URI
+#
+# CHECK: {"jsonrpc":"2.0","id":1,"result":[
+# CHECK-DAG: {"label":"a","kind":5}
+# CHECK-DAG: {"label":"bb","kind":5}
+# CHECK-DAG: {"label":"ccc","kind":5}
+# CHECK: ]}
 Content-Length: 44
 
 {"jsonrpc":"2.0","id":3,"method":"shutdown"}