This is not a "bug". The problem is in your design. For one, the pitch of the small sprocket is not the right pitch for your chain. I was able to get the chain and sprocket to rotate much more smoothly by making the small sprocket slightly smaller so that it matches the pitch of the chain. I also deleted the circle that sits behind the small sprocket. Then place a hinge (also called an axle) in the center of the sprocket. I also reduced the motor torque on the large sprocket. I used 100 Nm which seems to work well. Try those things and see if it works a little better.
EDIT: I noticed one more important thing. Your chain does not have consistent pitch. The pitch changes every 2 or 3 links. THAT'S BAD! I suggest that you remake the chain, and make the pitch between every link exactly the same! That should prevent the chain from exploding again!
EDIT2 - Check out my scene that I made for you which includes the suggestions that I made above. It does run much smoother, and the chain no longer explodes (as long as you do not pull on it too hard).
See Timing Belt. Also, make a chain by creating one link (some geometry with two axles), right clicking it and selecting "Use as chain". This will ensure that all links are the same length.