How to execute ajax function onbeforeunload?

I'm developing a php/javascript chat.

When the user logs in, his/her username is inserted in a MySQL table called queue. This insert returns the mysql_insert_id() that will be stored in a session variable called $_SESSION['CHAT_QUEUE_ID']

I need the MySQL table row to be deleted when the user closes the page.

I tried the following, but without success:

js file

window.onbeforeunload = closeSession;
function closeSession(){
    $.ajax({
        url: "/chat/process/chat.php",
        type: "GET"
    });
    return "disconnected";
}

chat.php

$delete= "DELETE FROM queue WHERE id = " . $_SESSION['CHAT_QUEUE_ID'];
// query, etc

Is there any way to do this?