It won't leave because it can't. It doesn't have enough room to flap its little wings and fly out. Birds generally sit on top of chimneys because it is nice and warm, particularly in the spring when they realize they should have stayed in Florida a little while longer. If they stay too long, the gas causes them to pass out and fall into the chimney. There should be a small opening on the inside wall of the chimney (it could have a door or sliding piece of metal). With your water heater and furnace turned off, you can open this cleanout and hope the bird will follow the light down. If he does not come out, she will definitely die from the gas fumes or starvation. You do need to get it out before it clogs the exhaust from the furnace or water tank and causes the gas to back up into your house. The last scenerio (forgive me bird lovers) No I can't say it...But once it is dead, you can remove it through the cleanout. I bet now you will go out and invest in a chimney cap.