You might want to check allow_single_deselect
option which adds a X button to blank it out:
//script
$(".my_select_box").chosen({
allow_single_deselect : true
});
//example html
<select class="my_select_box" data-placeholder="Pick a color..."
style="width:350px;" tabindex="1">
<option value="0"></option>
<option value="1">Blue</option>
<option value="2">Red</option>
</select>
From docs: "When set to true on a single select, Chosen adds a UI element which selects the first element (if it is blank)."