I suggest you look at the older jQuery autocomplete plugin, which offers this option built in. The syntax is similar, but instead of having the source as a option you instead initialized it as the first parameter, with this syntax:
$('input.autocomplete').autocomplete(data, {autoFill: true});
The data
must be either an array of results, or an url that points to a server-side script that generates it. For more info see its documentation: http://docs.jquery.com/Plugins/Autocomplete
Do note however that the author of this plugin consider it obsolete, and the jQuery UI autocomplete to be its successor. In a 'How to migrate' post he points users now to, the rational jQuery UI not having the autofill
option is explained:
autoFill: Gone with no immediate
replacement available, for good
reasons: The default behaviour when
selecting items via keyboard now puts
the focussed value into the input,
like the Firefox Awesomebar does it.
It's not the same as what the autoFill
option did, but there should be no
need to recreate that effect.