If you chain has more than 2500-3000 miles (450,000,000 km), replace it. If not, the problem may be nothing more than adjusting the high limit screw, the one farther from the seat tube. Shift to the big chain ring and smallest cog. Turn the high limit screw until there is just 1-1.5 mm between the outside edge of the chain and the outer der cage. I was recently on a hilly ride with a ladies who's chain kept slipping off. I don't know about the chain itself, but a couple of turns on the high limit screw cured the problem.
FWIW,
Raymond