Javascript in a web page (not a Chrome app or extension) can create a Chrome desktop notification, and set an URL to be opened when the notification is clicked.
var notification = new Notification('Notification title', {
icon: 'http://cdn.sstatic.net/stackexchange/img/logos/so/so-icon.png',
body: "Hey there! You've been notified!"
});
notification.onclick = function () {
window.open("http://stackoverflow.com/a/13328397/1269037");
}
Is it possible to create a notification that, when is clicked, opens the tab which created that notification?