The chain popping off even when it looks straight can be caused by a couple different things or a combination of things.
Are you using the old chain? If so, that could be the issue. I've experienced this on a couple mini's and also on my T-Bird. I tried aligning things, tightening the chain etc to no avail. It simply was stretched and wouldn't line up with the tooth spacing on the sprockets and it would come off. A new chain solved all issues.
Buy a new chain and try that.
Another issue is a known problem with T-Bird's. The engine mounting plate will twist or flex when TQ is applied. You need to reinforce it good and solid to stop that from happening.
Idling fast? Are you still using the governor? How did you hook up your throttle cable? Have you tried turning the idle screw counter clockwise to lower it?
Slap on a new chain and stiffen the motor plate and you'll be doing wheelies very soon.