Clear initialized Ajax-Chosen select to init it in some different way (e.g., changing url or GET/POST params). It's not as easy as it sounds...

clear_ajax_chosen_select.js

$(".chzn-select").html('<option></option>');
$(".chzn-select").trigger("liszt:updated");
$(".chzn-select").next('.chzn-container').find(".search-field > input, .chzn-search > input").unbind('keyup');
// then reinit ajax-chosen as usual
$(".chzn-select").ajaxChosen({ ... });