The old chimneys are normally OK for gas logs as they are. The removal of the layer of fire brick would keep you from ever using it as wood or coal burner again, but then, you shouldn't burn wood in these small boxes anyway. If you wanted to, you could certainly have the thing rebuilt for wood and the chimney would then have to be relined - they would use metal I would think. But I shudder at the cost of that.
Old fashioned vented gas logs would also be OK without the fire brick layer. I would at least have a sweep come out and check out the chimney. I would worry about it being cracked from settling or just having something flammable stuck in it, though the heat from the gas logs is a lot lower than coal or even a good wood fire.
The easiest is ventless gas logs. These are OK in the main public areas but not in bedrooms. You must use vented in bedrooms. Also, as mentioned by Gloria, you can either top cap it or close off the flue at the box. Capping it will keep water out of the chimney itself.
Save the Earth, it is the only planet that has chocolate!