That may happen due to chain/sprocket wear. The chain catches when rotating backward because it is elongated by wear (called stretch) and the sprockets have a hook in the forward direction that catch on the chain when rotated backward.
Look at your front sprocket and see if it has uniform symmetric U shaped teeth or if the teeth have a hook to the U shape. The rear may be the same way.
You probably need a new chain and sprockets. Both will be bad.
In spite of the cost, if your 350 is nice and you plan to keep your bike for a while or even restore it, spend the money for an O-ring chain along with your sprockets. Way less need for oiling making for less of a mess and at least two to three times the chain life.
If the bike's on the rough side and just a beginner to get you going or you simply can't afford the extra $50 or so, do the lower priced chain without O-rings.
Regardless of which type you buy, don't buy some no-name chain to save $10 bucks Buy an RK, DID, Tsubaki, or EK.
Here's a site with some commentary on chains.