Hi Ron,
I have successfully puu the AutoCompleteExtender within a user control without too much issue. You'll need to provide some more details around your problem so that I can diagnose what you might have done incorrectly.
You'll need to make sure that there is an appropriate ClientScriptManager control that can control the inclusion of supporting scripts so that things will work properly. Other than that, I'll need more detail before I can suggest any workarounds.
- Glav