Hmm, that's actually a good question. I think it's possible to do this by manually positioning the ListBox control just beneath the Edit control, then fill the list every time the text changes and hide it when the Edit control loses its focus. Although it'd require quite some code to get it working I'm afraid.
I'll try to find time to have a look at this today.
Hmm, seems like I misinterpreted your idea of auto-completion. I was thinking in the likes of a search bar where you'd get suggestions in a list below it. (see the Firefox search bar for example)
What you're asking for is an IntelliSense feature like we can see in the Plus! Live script editor or Visual Studio. This is much harder to do I'm afraid...
Anyway, if anyone was looking for something which can do this...
...check out the attachment.