Is this for cosplay at a convension or just for you? a bicycle chain and sprockets with a small motor would work but I doubt you would be allowed into cons with it. For safety I'd use lego chain and sprockers. The lego motor would run it too. It would look quite good as the links are about the size of a chainsaws chain. Look under technic lego chain if you fancy it.
Hope that helps.
You may want to consider sound vs animation. It will also be much more simple all around. A decent sound file of a chainsaw through a decent mini sound system with speakers mounted inside the chainsaw body would likely get people moving. For instance ive made many prop hand held light up stun guns but the ones that make people jump everytime are the ones with a little motor and zip ties on it that make the "brrrzap" noise. Works everytime.
I tried to sort this out myself when I did my Gears of War costume a few years back. I didn't get very far, but my plan was to pick up one of those motorized toy chainsaws and gut its innards to fit my purpose. I actually had a similar smaller chainsaw toy I found and took it apart to examine the mechanics. It had a rubber belt that ran around a series of rollers (powered by gears) with rubber 'teeth' molded onto the outside of the belt. The problem I had was I was trying to make the Lancer gun, and the toy I bought had a far too short 'chain' for my purpose.
I looked into something like this too: ( http://www.partycity.com/product/animated+chainsaw.do?page=2&navSet=350295 ) but it didn't fit my particular needs, but maybe it would work for your project with a bit of work.
I have that chainsaw, and it's remarkably loud for a fake one! The chain moves very slowly but it worked for my Leatherface costume a few years ago:
http://i14.photobucket.com/albums/a301/bonzohart/LeatherfaceMeweb.jpg
The entire rig is 30" -- but the blade is 15". Here's a pretty good review of one:
https://www.youtube.com/watch?v=HVnjPF9tox0
Get one!