Having seen a 'chainsaw' instructable which was not a chainsaw, I started thinking. I had some Lego bits, including:
A motor (4.5v)
Some gear wheels
Some chain links
And some other general bits.
These parts are required, as pictured.
The tricky part was the saw teeth...
Step 1: Saw Teeth
These are the most tricky part, which is why I started on them first.
If you examine Lego chain-links, you will see that they interlock with pins spaced 6.5mm apart. There's enough clearence to get something very thin between the joints to be fixed on the same pins:
Aluminium beer-can, easily cut with scissors & sharp knives (do be careful).
A knife blade
A piece of stiff wire (from an umbrella)
A picture nail
An abrasive stick (coarse corundum, probably)
A piece of wood
Please view the pictures for the method.