Improper sprocket alignment is the biggest cause of chains falling off. The next cause is a chain that is adjusted too loose. There should be 1/2 inch of free play on the slack side of the chain.
The factory chains are also known to be trash right out of the box.
It should also be noted that some of the sprockets, both engine and rear wheel, come from the factory with burrs on the teeth that need to be smoothed out. Also on some of the the engine sprockets the valleys between the teeth are machined too deep and the tips of the teeth need to be very carefully filed just a little bit shorter to fix this problem.
This must be carefully looked at though. Do not assume any of the problems are actually there and merrily file away at the sprockets. Look closely at how the chain wraps around the teeth and see if it is getting hung up before modifying the sprockets.
The factory chains are also known to be trash right out of the box.
It should also be noted that some of the sprockets, both engine and rear wheel, come from the factory with burrs on the teeth that need to be smoothed out. Also on some of the the engine sprockets the valleys between the teeth are machined too deep and the tips of the teeth need to be very carefully filed just a little bit shorter to fix this problem.
This must be carefully looked at though. Do not assume any of the problems are actually there and merrily file away at the sprockets. Look closely at how the chain wraps around the teeth and see if it is getting hung up before modifying the sprockets.