What usually happens is the mortar will breakdown from where the chimney leaves the attic. This is caused by the temperature difference creating moisture and chemical breakdown from the burned fuel. I recommend taking the chimney down to the flashing and replacing it inside and out. You can use either a type S mortar (1 part portland 1/2 part lime 4 1/2 sand)or a type N ( 1 part portland 1 part lime 6 parts sand). You can buy this in bags by type and just add sand. Check the rest of the chimney for cracks inside and out but it will most likely be just the top and should be simple to replace.