diff --git a/cmd/tailscaled/depaware.txt b/cmd/tailscaled/depaware.txt
index 7e3e88fd7..5b72d243a 100644
--- a/cmd/tailscaled/depaware.txt
+++ b/cmd/tailscaled/depaware.txt
@@ -275,7 +275,9 @@ tailscale.com/cmd/tailscaled dependencies: (generated by github.com/tailscale/de
         golang.org/x/net/dns/dnsmessage                              from net+
         golang.org/x/net/http/httpguts                               from net/http+
         golang.org/x/net/http/httpproxy                              from net/http
-        golang.org/x/net/http2/hpack                                 from net/http
+        golang.org/x/net/http2                                       from golang.org/x/net/http2/h2c+
+        golang.org/x/net/http2/h2c                                   from tailscale.com/ipn/ipnlocal
+        golang.org/x/net/http2/hpack                                 from net/http+
         golang.org/x/net/idna                                        from golang.org/x/net/http/httpguts+
         golang.org/x/net/ipv4                                        from golang.zx2c4.com/wireguard/device
         golang.org/x/net/ipv6                                        from golang.zx2c4.com/wireguard/device+
diff --git a/ipn/ipnlocal/peerapi.go b/ipn/ipnlocal/peerapi.go
index 1746a4d7e..1fa9e2122 100644
--- a/ipn/ipnlocal/peerapi.go
+++ b/ipn/ipnlocal/peerapi.go
@@ -46,6 +46,10 @@
 
 var initListenConfig func(*net.ListenConfig, netaddr.IP, *interfaces.State, string) error
 
+// addH2C is non-nil on platforms where we want to add H2C
+// ("cleartext" HTTP/2) support to the peerAPI.
+var addH2C func(*http.Server)
+
 type peerAPIServer struct {
 	b          *LocalBackend
 	rootDir    string // empty means file receiving unavailable
@@ -492,6 +496,9 @@ func (pln *peerAPIListener) serve() {
 		httpServer := &http.Server{
 			Handler: h,
 		}
+		if addH2C != nil {
+			addH2C(httpServer)
+		}
 		go httpServer.Serve(&oneConnListener{Listener: pln.ln, conn: c})
 	}
 }
diff --git a/ipn/ipnlocal/peerapi_h2c.go b/ipn/ipnlocal/peerapi_h2c.go
new file mode 100644
index 000000000..3888db8d9
--- /dev/null
+++ b/ipn/ipnlocal/peerapi_h2c.go
@@ -0,0 +1,22 @@
+// Copyright (c) 2021 Tailscale Inc & AUTHORS All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:build !ios && !android
+// +build !ios,!android
+
+package ipnlocal
+
+import (
+	"net/http"
+
+	"golang.org/x/net/http2"
+	"golang.org/x/net/http2/h2c"
+)
+
+func init() {
+	addH2C = func(s *http.Server) {
+		h2s := &http2.Server{}
+		s.Handler = h2c.NewHandler(s.Handler, h2s)
+	}
+}