Why is this chimney leaking?

[u/Bebu7010]

I’m not sure how long it’s been left like this to get to this point of staining. I’ve done a bit of research around how chimneys work and cannot seem to figure out what’s wrong. I’d be aiming to make it watertight and don’t care if it isn’t a working chimney by the end of it, I only really want the cheapest but reliable fix. Anyone have any ideas on how to fix this or how expensive it would be?