We\'ve tested the Jquery UI (jquery-ui-1.8.10.custom.min.js) Autocomplete function in a simple HTML page which worked.
We then copy the same code into an Asp.net User C
That error usually means that jquery or the plugin hasn't yet been loaded. Check that you're function call isn't getting hit before the document is loaded:
$(function(){
var $searchBox = $('#mysearchBox');
$searchBox.autocomplete(...);
});
Also check that the path to the javascript files are correct. Firebug or google chrome developer tools are useful for checking both of these issues.