Check that you don't have the chain safety brake on, check by pulling back on the lever positioned in front of the chainsaw forward hand grip. Double check by pushing forward until it clicks then back until it releases.
Check air cleaner is clean.
If those checks are ok, then maybe the low speed mixture screw needs adjusting. Try screwing in until the screw marked with a (L) found on the side of the chainsaw near carby until it lightly bottoms out (don't tighten and count the number of turns so that you can return it to the set position if all else fails). Once bottomed, unscrew 1 1/2 to 1 3/4 turns and try starting the saw again. If the saw idles pull the trigger in to slightly increase and hold revs and at the same time screw the (L) mixture screw out the saw may die in revs or rev higher. Experiment both ways in and out, I'm talking less than a quarter of a turn at a time. You will find a spot where the saw runs cleanly and revs pickup quickly when the trigger is quickly pulled half way.
If this does not work then one of both of the crankshaft seals might be worn and leaking if the saw is quite old of being sitting around for many years.
Best of luck
onyamichael, February 2013