Bicycle Tutor

Just bought an old wicked fat chance, cleaned it up and the only issue at this point is the front will go to the big chainring but not stay. It just drops to the small chainring, unless you keep your thumb on it! What adjustment am I looking for?

I would take a look at this tutorial if you have not done so already: http://bicycletutor.com/adjust-front-derailer/ It may be that you can adjust the screws and try to see if you can center the chain better. Depending on what kind of shifters you have, it may be a matter of changing the tension if there are barrel adjusters if you have the rapid fire style shifters and since you mentioned thumb, I hope I am on the right track.
Also, I had a problem similar to this a few years ago and it turned out I had a bad bottom bracket. Check for play by pushing back and forth on the cranks and see if there is movement. That can affect how well a chain stays on as well. If there is play, I would pop it open and look at it. If it is an older bike, chances are it is a cup and cone style BB. If it is a cartridge style, I am pretty sure it will need to be replaced if that is indeed the problem.