This is exactly what it sounds like. I looked around for a solution, but got tired of that quite quickly so just wrote my own. I use a plain textbox and a hidden listbox (SELECT box). When the textbox gets focus the list is displayed right under it, just like a real combo box.
This depends on the lovely behaviour.js library. It is a light dependency -- easily removed probably. But I like it and recommend you use it for other stuff anyway!
See a demo at http://thelackthereof.org/dev/dhtml_combo/combo.html