i'm assuming that you have a list of items on one side, and when the user selects them and clicks "transfer" it copies the selected items over to the right side. While technically not ajax unless you send the request off to the server, this is possible.
Give each element in the list an id, and when you click on an item, run some js to note the id that has been clicked (easiest way with so many list items). When you click transfer, pull the array from the function (best done using an object) and in that array will be all the values, this bypasses having to check each item if it has been checked. Though, i'd suggest writing the items as a js script as well, because it would create a LOT more traffic. (Maybe you should think of a way to use AJAX to get around downloading so many items?)