Must I have a chimney?

[Mark Forest]

I have a house where the chimney is falling apart and the estimates to take it down and rebuild are over $2K. I just have a furnace and hot water heater exhausting through it. The gas is off. Is there a reason I must replace the chimney with brick? Isn’t there a cheaper way that still works? I do not care about appearance in this house.

Also I would like to save money by DIY the demolition. As I said there is not exhaust running thorough it now, so do I just go up there with a hammer and start knocking out bricks?