I recently purchased a small chain light switch for a light I have above kitchen sink, the one that was there, stopped switching, so I I purchased another one, however the one I purchased has 3 wires instead of the old 2 wire---the third wire on the new switch is red and I believe, that it is for a fan, which I do not have, can I still use this 3 wire switch?

Yes but you will have a dead spot when you pull the chain if you don't use the red. However, you can tie the red and black together and then have the light on for 2 pulls.