Check the leadwork at the back and sides of the chimney
You can often see the front flashing from the ground, but the hidden leadwork around the sides and rear may be where the problem sits.
Look at the chimney itself
Open pointing and cracked flaunching can let rain soak into the masonry.
Unused flues can stay damp
Moisture inside a chimney breast on cold dry days can be condensation rather than a roof leak.