Please, please, PLEASE don't try this!
I really can't tell you how bad an idea this is. Really.
Look, tires aren't made of solid rubber. If they were, they'd behave more like balloons than tires: the air pressure would cause them to inflate, stretch, and come off the rim.
And that's the best case scenario.
To keep that from happening, there are strings and wires woven in to the body of the tire. Bands or 'belts' of nylon and steel are layered inside the tire to help them keep their shape.
A chainsaw is designed to cut through wood. Just wood. The teeth are, if you look closely, shaped like hooks. They are sharpened on the inside edge of the hook, but they're still HOOKS. They will cut through the rubber with some difficulty, and they might cut some of the belts, but mostly they'll catch those belts and tangle them around the blade.
The BEST case scenario then, is that you stall the engine on the chainsaw and have to tear it down and spend an hour untangling all the strings and cables.
I'll leave to your imagination what the worst-case scenario might be.