A Greasemonkey script to show notifications when there is any new mail in an Office 365 Outlook Web App tab.

office_365_notifications.js

// ==UserScript==
// @name       Office 365 notifications
// @namespace  http://use.i.E.your.homepage/
// @version    0.1
// @description  Show a Google Chrome notification when there is any unread mail.
// @match      https://*/owa/*
// @copyright  2012+, You
// ==/UserScript==

var current_unread_count = 0;

function checkForUpdate() {
    var clsElements = document.querySelectorAll("._n_D6");
    var max = clsElements.length;
    var unread_count = 0;
    
    for (var i=0; i<max; i++) {
        var element = clsElements[i];
        var unread_count_id = element.id.split(".")[0] + ".ucount";
        if (document.getElementById(unread_count_id)) {
            unread_count += 1;
        }
    }
    
    if (unread_count != current_unread_count) {
        current_unread_count = unread_count;
        if (unread_count > 0) {
            GM_notification("You've got mail!", "Unread mail", null, 1000);
        }
    }    
}

setInterval(checkForUpdate, 1000);