Our local courthouse is attempting to raise money for renovations. The bank hired a local artist to paint a picture of various scenes in the area. We, along with other businesses, want to sell chances on the painting and give all proceeds to the courthouse fund. Anyone could purchase a chance and it isn't at all related to opening an account or any other banking aspect. Would this be considered a lottery?

This is a lottery/raffle. Do a search on lottery and/or raffle and you will find many discussions as to what is and is not. Also, you may need to check your state laws.

You can provide the painting, but should probably not sell tickets.

I agree...you could provide the painting but not sell the tickets or "advertise" the lottery.