Chain coming off at the foot of a hill is the most annoying thing! Assuming the tension is still ok to get you into the big ring, all you should need to do is adjust the low limit screw for the front derailleur to, as the name implies, limit the distance the derailleur can move, to make it impossible to pull the chain off the small ring.
Thanks! I have to admit the whole gear system is a little bewildering to a newbie.
Worst part about the chain coming off is getting grease all over my hands and soiling that perfectly white tape on the bars...