diff --git a/http2/http2.go b/http2/http2.go
index 2e27b093..dd6824dd 100644
--- a/http2/http2.go
+++ b/http2/http2.go
@@ -36,6 +36,7 @@ var (
 	VerboseLogs    bool
 	logFrameWrites bool
 	logFrameReads  bool
+	inTests        bool
 )
 
 func init() {
diff --git a/http2/http2_test.go b/http2/http2_test.go
index 22c2ace8..52487764 100644
--- a/http2/http2_test.go
+++ b/http2/http2_test.go
@@ -27,6 +27,7 @@ func condSkipFailingTest(t *testing.T) {
 }
 
 func init() {
+	inTests = true
 	DebugGoroutines = true
 	flag.BoolVar(&VerboseLogs, "verboseh2", VerboseLogs, "Verbose HTTP/2 debug logging")
 }
diff --git a/http2/server.go b/http2/server.go
index 808b0111..11d3b65b 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -1858,16 +1858,19 @@ func (sc *serverConn) sendWindowUpdate32(st *stream, n int32) {
 	}
 }
 
+// requestBody is the Handler's Request.Body type.
+// Read and Close may be called concurrently.
 type requestBody struct {
 	stream        *stream
 	conn          *serverConn
-	closed        bool
+	closed        bool  // for use by Close only
+	sawEOF        bool  // for use by Read only
 	pipe          *pipe // non-nil if we have a HTTP entity message body
 	needsContinue bool  // need to send a 100-continue
 }
 
 func (b *requestBody) Close() error {
-	if b.pipe != nil {
+	if b.pipe != nil && !b.closed {
 		b.pipe.BreakWithError(errClosedBody)
 	}
 	b.closed = true
@@ -1879,12 +1882,15 @@ func (b *requestBody) Read(p []byte) (n int, err error) {
 		b.needsContinue = false
 		b.conn.write100ContinueHeaders(b.stream)
 	}
-	if b.pipe == nil {
+	if b.pipe == nil || b.sawEOF {
 		return 0, io.EOF
 	}
 	n, err = b.pipe.Read(p)
 	if err == io.EOF {
-		b.pipe = nil
+		b.sawEOF = true
+	}
+	if b.conn == nil && inTests {
+		return
 	}
 	b.conn.noteBodyReadFromHandler(b.stream, n, err)
 	return
diff --git a/http2/server_test.go b/http2/server_test.go
index 1295b433..22aabf21 100644
--- a/http2/server_test.go
+++ b/http2/server_test.go
@@ -3372,3 +3372,27 @@ func TestUnreadFlowControlReturned_Server(t *testing.T) {
 	}
 
 }
+
+// grpc-go closes the Request.Body currently with a Read.
+// Verify that it doesn't race.
+// See https://github.com/grpc/grpc-go/pull/938
+func TestRequestBodyReadCloseRace(t *testing.T) {
+	for i := 0; i < 100; i++ {
+		body := &requestBody{
+			pipe: &pipe{
+				b: new(bytes.Buffer),
+			},
+		}
+		body.pipe.CloseWithError(io.EOF)
+
+		done := make(chan bool, 1)
+		buf := make([]byte, 10)
+		go func() {
+			time.Sleep(1 * time.Millisecond)
+			body.Close()
+			done <- true
+		}()
+		body.Read(buf)
+		<-done
+	}
+}