This problem could be caused by old/cracked roofing shingles, heavy winds with rain, old or improper chimney/roof flashing and counter flashing, cracks between the bricks needing repair and repointing, cracks or damage in the concrete "cap" at the top of your chimney or its lack of waterproofing, degraded mortar in the liner flue tiles, and/or the lack of a metal chimney cap. These are some possibilities.
I would go on the roof (only if you are comfortable doing this and know how to do it safely) and inspect the chimney for obvious problems such as cracks in the mortar or degraded mortar. Also check the mortar chimney "cap" to see if it is cracked or that it isn't sealed well on the edges. Also check the flashing and the shingle condition around the chimney. Then if you see something obvious then write us back for what to do. Often the installation of a quality, well fit chimney cap can eliminate water infiltration problems, but you still need to check those other items.