Is this chosen module support entity reference field ?

Yes, just use the "Select list" widget instead of an autocomplete widget.

If you have trouble finding this after switching (like I had, after switching from checkboxes to select list) make sure you look carefully. The "use chosen" option is in a collapsed fieldset.

Thank you for these answers!
And to complete, the select list to apply "Chosen" on the field is:
- on the field's 'Edit' tab
- Under the label 'Apply Chosen to the select fields in this widget?", choose "Apply"

I don't know what the 'No preference' option is what for...

Will this make pass text typed into entityreference view and get back data just like autocomplete or it just searched pre-rendered select list only?

setup:
entityreference field of type node with entityrefrence view is configured as source. This work well with autocomplete widget(core) but shows nid in parentheses. To avoid this and show x button to remove selected element I want it to test with chosen.