Steve,
Ah those pesky little chain saw engines! There are a TON of Youtube videos that go step by step through this issue. Since it runs and is therefore probably not an ignition problem, the carb/fuel is the problem and could be a stiff pump diaphragm, out of adjustment (likely if you are lucky), fuel lines are old and sucking air making the mixture too lean and need to be replaced. I’ve had to replace lots of fuel lines. I buy it in bulk. Could be a bad pick up in the tank which is easy to check, and usually isn’t the problem.