SO jQuery Fiddle

Test Fiddle mainly for SO Questions jQuery 1.4.3, UI 1.8.5

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.5/themes/ui-lightness/jquery-ui.css">
<div class="selector">
<input type=checkbox name="hello" value="test"/>
<input type=checkbox name="bye" value="test"/>
<input type=checkbox name="no" value="test2"/>
<input type=checkbox name="no no" value="test2"/>
</div>

JavaScript

$(".selector").children("input:checkbox").click(function(){
var test = $(this).val();
if(test=="test"){
$(this).attr('checked', false);
//now check that single checkbox that was clicked, so that in the end, we end up with only 1 checkbox being checked
}
});