Most commonly in pre-fabricated (metal) units, this can point to a problem with the chase cover, which covers the opening of the chimney at the exterior. If left untreated, this could lead to extensive corrosion damage to the fireplace and require it’s replacement. There can also be other sources of water intrusion, which we can diagnose in an inspection.
With masonry chimneys, the source of leaking can be the lack of a proper rain cap, a cracked crown, loose or missing mortar joints, among others. In both cases, preventative maintenance can save you a large expense down the road.