static native void sendMessageToChromeExtension() /*-{
    chrome.runtime.sendMessage(...);
}-*/;

Cannot read property 'sendMessage' of undefined

"externally_connectable": {
    "matches": ["*://*.example.com/*"]
}

static native void sendMessageToChromeExtension() /*-{
    $wnd.chrome.runtime.sendMessage(...);
}-*/;