The amount of smoke emanating from a properly installed, sharpened, and lubricated chain should be very little.
After several minutes of working tough wood the chain and sword will get warm (despite properly lubrication) & water vapor/steam from humidity wood might look like smoke.
If it really is smoke, you are doing something wrong. Take a course and get certified. Chain saws are not toys and can cause you as wellas others harm if used improperly.
Chances are the chain is dull so it's grinding it's way through the wood instead of cutting. Maybe the chain is on backwards lol,I've seen it before. There is also the possibility of over spill of chain lubricant that got onto the muffler which will make smoke. If the chainsaw is making smoke without you cutting wood then it's not the chain.
If your unfilmilar with using a chainsaw,then it's wise to go on YouTube and check out some videos on how and how not to use a chainsaw. They can be lots off pleasure/fun using one but can also be very painful/disappointment at the same time if you have no experience or the chainsaw isn't in good running condition or using a dull chain.