As mentionned in some more recent answers, the plugin now implemements an option to change the search behavior:
search_contains: true
Options documentation
The plugin does not provide an option to change the search method behavior.
If you’re willing to change the plugin source itself, here’s a way to do it.
The method that makes the search in the plugin is Chosen.prototype.winnow_results. It uses a regular expression that matches text that “starts with” the search term:
// "^": means "starts with"
// "searchText" is the text in the search input (it is just cleaned up don't be scared)
regex = new RegExp('^' + searchText.replace(/[-[\]{}()*+?.,\\^$|#\s]/g, "\\$&"), 'i');
Change it to:
regex = new RegExp(searchText.replace(/[-[\]{}()*+?.,\\^$|#\s]/g, "\\$&"), 'i');
DEMO