Firefox allows the request because it accepts requests to the local file system (ie. the file:// protocol) if they originate from there too. However Chrome denies all XMLHttpRequests to file:// urls.
Note that you cannot make an AJAX request to the local file system from an external domain in either browser - it would be a massive security flaw if you could.
For this AJAX request to work in Chrome you need to make the request to a webserver. If you're on Windows you can easily install IIS or WAMP on your local machine.
Note that it is possible to enable a setting in Google Chrome which allows requests to the local file system from the browser, but it's really not a good idea to use it. If you decide you want to go ahead and do this anyway, a guide can be found here.
