It has to be the carburetor, or an air leak between the carburetor and cylinder. On those small engines with chainsaw carburetors, the main suspects are the intake filter, and the pump diaphragm, but many other things can go wrong as well. What kind of carburetor is it? If we can find the carburetor manual, we can work from that, making life quite a bit easier. It is probably Walbro, Tillotson or Zama. Find out which, and which model, please.