Chimneys are subject to exposure from the elements, and cannot last forever. Can you get by without yours?
If your chimney is in the middle of the house, as opposed to an outside wall, and if you don’t have a wood-burning fireplace and it is starting to show its age, consider taking it down to below the roof altogether.
The process is fairly straightforward; wearing your safety gear, place plywood on the roof to protect the shingles. Hammer the bricks loose and toss them onto a tarp on the ground. Take your time and aim well; bricks are heavy and falling bricks can cause a lot of damage. Keep going until the top of the chimney is well below the roof edge. Is there a metal vent from the furnace or water heater? The patched roof will need to accommodate that vent.
Using aluminum sheets, patch the gap at the top of the remaining chimney. This is very important, because warm air from the house will get into the attic, where it doesn’t belong. See attic bypasses.