In Chrome, how can I see what AJAX requests are being made?
In Firefox I use Firebug and I can see any background AJAX request that are made.
Open the developer tools with Ctrl-Shift-i, or via the menu at Wrench/Tools/Developer tools:

Click on the Network Tab:

Click on the "XHR" link at the bottom of the list to filter the results to only AJAX requests:

Click on a request at the left to select it and use the "Headers", "Content", "Cookies" and "Timing" tabs for that request to see more details:

You can use the
button in the bottom left of the tools to open the tools in their own window if you like.