If you have a brand new mountain bike and you chain is dropping then take it back to the shop and ask them to check and see if there are any issues. It's not considered unusual for a the shifting system to need adjustment after the first few hundred miles. As well spokes on your wheels should be checked to make certain that some haven't become too loose. Usually this is just a one time thing, but many will have their bikes checked every year or two if their owner isn't an avid DIYer.

However you might drop a chain with bad shifting technique. Especially if you are riding at a very low cadence. Shifts need a certain amount of crank rotation in order to complete. if your cadence is so slow that you can't complete a full revolution of the crank smoothly then you've waited to long to shift. So next time shift sooner. Well before you start struggling to pedal. Once your cadence drops below 50 - 60 rpm, shifting will be disastrous. Try to keep 70 rpm or better till you get to that lowest possible gear combo. I tend to keep 85 - 90 rpm when going up hills till I get to that lowest gear combo and can shift without having to let up on the power very much if any at all.

If you wind up walking your bike before your gear combo is in the lowest possible gear, then that also is a good indication that you are waiting to long before shifting to a lower gear ratio. Pedaling should be stupidly easy! Grunting and straining to get up a hill with all force your leg muscles can manage is not the way to ride your bike. It won't do anything for your fitness or make you good at riding. You should only grunt and have to strain on very steep hills after you have reached that lowest possible gear combination just before you have to get off the bike and walk.

If you are using your mountain bike on paved roads, then I doubt that there is any paved road steep enough to be outside of the normal gearing range of the bike.