Attributes aren't written out for each Item.
Can't you add the onClick to the CBL it-self and loop thru the elements in JS ??
CheckBoxList1.Attributes["onClick"] = "return checkPIME(this);";
-or-
You could make a control(inherit from CBL) and write out the attributes for each element I guess.
I did that for a ListBox to show the color attrib.
Sample: www.gotdotnet.com/.../keywordsrch.aspx%20with%20color%20attribute