jQuery validate ignores the hidden element, and since the Chosen plugin adds visibility:hidden
attribute to the select, try:
$.validator.setDefaults({ ignore: ":hidden:not(select)" }) //for all select
OR
$.validator.setDefaults({ ignore: ":hidden:not(.chosen-select)" }) //for all select having class .chosen-select
Add this line just before validate()
function. It works fine for me.