I actually coded a control like this for a web framework last year some time. I literally layered a textbox with no borders over the top of the select box control. The drop down button of the select was sticking out past the edge of the textbox. I also had a 3rd hidden textbox that contained the value I cared about when the form was submitted to the server.

As the user typed into the textbox, I searched the list for the next match and highlighted the remaining auto-filled text so they could keep typing normally over it.

If they select something from the dropdown, I fill in the textbox.

This leaves it up to the user how they want to use the control. I called it an Editable Combo box. This is pretty tricky. First, there are problems with cross-browser rendering and layering, not that these ever go away. Also, this would allow the user to enter values that don't exist in the dropbox. Of course, you could write code that would validate that and not allow it.

Good luck.