diff --git a/src/net/http/readrequest_test.go b/src/net/http/readrequest_test.go
index 1225d97edbe63c..4bf646b0a63ce0 100644
--- a/src/net/http/readrequest_test.go
+++ b/src/net/http/readrequest_test.go
@@ -380,6 +380,27 @@ var reqTests = []reqTest{
 		noTrailer,
 		noError,
 	},
+
+	// http2 client preface:
+	{
+		"PRI * HTTP/2.0\r\n\r\nSM\r\n\r\n",
+		&Request{
+			Method: "PRI",
+			URL: &url.URL{
+				Path: "*",
+			},
+			Header:        Header{},
+			Proto:         "HTTP/2.0",
+			ProtoMajor:    2,
+			ProtoMinor:    0,
+			RequestURI:    "*",
+			ContentLength: -1,
+			Close:         true,
+		},
+		noBody,
+		noTrailer,
+		noError,
+	},
 }
 
 func TestReadRequest(t *testing.T) {
diff --git a/src/net/http/request.go b/src/net/http/request.go
index 9cf2d2576fbe3e..d9ebb26dfc6123 100644
--- a/src/net/http/request.go
+++ b/src/net/http/request.go
@@ -343,6 +343,12 @@ func (r *Request) multipartReader() (*multipart.Reader, error) {
 	return multipart.NewReader(r.Body, boundary), nil
 }
 
+// isH2Upgrade reports whether r represents the http2 "client preface"
+// magic string.
+func (r *Request) isH2Upgrade() bool {
+	return r.Method == "PRI" && len(r.Header) == 0 && r.URL.Path == "*" && r.Proto == "HTTP/2.0"
+}
+
 // Return value if nonempty, def otherwise.
 func valueOrDefault(value, def string) string {
 	if value != "" {
@@ -794,6 +800,16 @@ func readRequest(b *bufio.Reader, deleteHostHeader bool) (req *Request, err erro
 		return nil, err
 	}
 
+	if req.isH2Upgrade() {
+		// Because it's neither chunked, nor declared:
+		req.ContentLength = -1
+
+		// We want to give handlers a chance to hijack the
+		// connection, but we need to prevent the Server from
+		// dealing with the connection further if it's not
+		// hijacked. Set Close to ensure that:
+		req.Close = true
+	}
 	return req, nil
 }
 
diff --git a/src/net/http/serve_test.go b/src/net/http/serve_test.go
index c49262201a872f..638ba5f48f6373 100644
--- a/src/net/http/serve_test.go
+++ b/src/net/http/serve_test.go
@@ -741,6 +741,13 @@ func TestHandlersCanSetConnectionClose10(t *testing.T) {
 	}))
 }
 
+func TestHTTP2UpgradeClosesConnection(t *testing.T) {
+	testTCPConnectionCloses(t, "PRI * HTTP/2.0\r\n\r\nSM\r\n\r\n", HandlerFunc(func(w ResponseWriter, r *Request) {
+		// Nothing. (if not hijacked, the server should close the connection
+		// afterwards)
+	}))
+}
+
 func TestSetsRemoteAddr_h1(t *testing.T) { testSetsRemoteAddr(t, h1Mode) }
 func TestSetsRemoteAddr_h2(t *testing.T) { testSetsRemoteAddr(t, h2Mode) }
 
@@ -3877,10 +3884,17 @@ func TestServerValidatesHostHeader(t *testing.T) {
 		{"HTTP/1.0", "", 200},
 		{"HTTP/1.0", "Host: first\r\nHost: second\r\n", 400},
 		{"HTTP/1.0", "Host: \xff\r\n", 400},
+
+		// Make an exception for HTTP upgrade requests:
+		{"PRI * HTTP/2.0", "", 200},
 	}
 	for _, tt := range tests {
 		conn := &testConn{closec: make(chan bool, 1)}
-		io.WriteString(&conn.readBuf, "GET / "+tt.proto+"\r\n"+tt.host+"\r\n")
+		methodTarget := "GET / "
+		if !strings.HasPrefix(tt.proto, "HTTP/") {
+			methodTarget = ""
+		}
+		io.WriteString(&conn.readBuf, methodTarget+tt.proto+"\r\n"+tt.host+"\r\n")
 
 		ln := &oneConnListener{conn}
 		go Serve(ln, HandlerFunc(func(ResponseWriter, *Request) {}))
@@ -3896,6 +3910,45 @@ func TestServerValidatesHostHeader(t *testing.T) {
 	}
 }
 
+func TestServerHandlersCanHandleH2PRI(t *testing.T) {
+	const upgradeResponse = "upgrade here"
+	defer afterTest(t)
+	ts := httptest.NewServer(HandlerFunc(func(w ResponseWriter, r *Request) {
+		conn, br, err := w.(Hijacker).Hijack()
+		defer conn.Close()
+		if r.Method != "PRI" || r.RequestURI != "*" {
+			t.Errorf("Got method/target %q %q; want PRI *", r.Method, r.RequestURI)
+			return
+		}
+		if !r.Close {
+			t.Errorf("Request.Close = true; want false")
+		}
+		const want = "SM\r\n\r\n"
+		buf := make([]byte, len(want))
+		n, err := io.ReadFull(br, buf)
+		if err != nil || string(buf[:n]) != want {
+			t.Errorf("Read = %v, %v (%q), want %q", n, err, buf[:n], want)
+			return
+		}
+		io.WriteString(conn, upgradeResponse)
+	}))
+	defer ts.Close()
+
+	c, err := net.Dial("tcp", ts.Listener.Addr().String())
+	if err != nil {
+		t.Fatalf("Dial: %v", err)
+	}
+	defer c.Close()
+	io.WriteString(c, "PRI * HTTP/2.0\r\n\r\nSM\r\n\r\n")
+	slurp, err := ioutil.ReadAll(c)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if string(slurp) != upgradeResponse {
+		t.Errorf("Handler response = %q; want %q", slurp, upgradeResponse)
+	}
+}
+
 // Test that we validate the valid bytes in HTTP/1 headers.
 // Issue 11207.
 func TestServerValidatesHeaders(t *testing.T) {
diff --git a/src/net/http/server.go b/src/net/http/server.go
index 17c2890aa7b351..5718cafbc3d728 100644
--- a/src/net/http/server.go
+++ b/src/net/http/server.go
@@ -714,7 +714,8 @@ func (c *conn) readRequest() (w *response, err error) {
 	c.r.setInfiniteReadLimit()
 
 	hosts, haveHost := req.Header["Host"]
-	if req.ProtoAtLeast(1, 1) && (!haveHost || len(hosts) == 0) {
+	isH2Upgrade := req.isH2Upgrade()
+	if req.ProtoAtLeast(1, 1) && (!haveHost || len(hosts) == 0) && !isH2Upgrade {
 		return nil, badRequestError("missing required Host header")
 	}
 	if len(hosts) > 1 {
@@ -748,6 +749,9 @@ func (c *conn) readRequest() (w *response, err error) {
 		handlerHeader: make(Header),
 		contentLength: -1,
 	}
+	if isH2Upgrade {
+		w.closeAfterReply = true
+	}
 	w.cw.res = w
 	w.w = newBufioWriterSize(&w.cw, bufferBeforeChunkingSize)
 	return w, nil