it is fully depends on what you ready to compromise.
1. you use select, and when user clicks on it, you display a popup div with edit element, allowing user to enter the value. When div looses focus, you hide it and chnage the text of the option.
2. you don't use select, but use a div instead to mimic select functionality + little extra, like editing. example:
http://www.devsoftware.com/dhtmlTest/select.html