Originally Posted by Bikewer
Two things are usually to blame for the chain coming off the cogs. Ist is an improperly adjusted limit screw on the rear derailleur. Lots of novices like to fool with these for some reason. The other is a bent DR hanger.
Easiest to check for either condition with the chain off; you should easily find derailleur setup instructions on the Park Tool site.
Ditto what he said but if the bike is a new build and you haven't wrecked or dropped it on the right side the derailleur shouldn't be bent.
The limit adjust screws are fairly easy to set. The H limit should be set so that the upper derailleur pulley is centered under the outside edge of the small cog. The L limit should be set so that the upper derailleur pulley is centered with the large cog. After doing that all you need to do is set the b-adjust, located at the top of the derailleur where it mounts to the frame, so that you have about 1/4" seperation between the teeth of the large cog and the upper derailleur pulley. You'll probably find that is set properly. Shift the bike from smallest to largest cog and back and make sure that it shifts cleanly to each cog. Now go for a ride, you're done!