Check all areas around your chimney, both inside the home and outside. Water infiltration will be more obvious at the interior as you will see stained, loose or swollen drywall. Other materials will exhibit similar problems so look carefully. Get up on the roof and give the chimney careful examination. The biggest culprit can be the chimney cap. If it is poured concrete or cast stone or natural stone, check for cracks, caulking problems or dislodging of the cap.
If your chimney is brick, check for missing mortar, cracks in the mortar or spalled brick (spalling is the faces of the brick freezing off due to moisture penetration). Also, inspect the flashing where the brick joins the roof (hopefully you DO have flashing - if not you definitely need it.) Check the flashing to see that it is not loose or hanging off the brick and that it is properly secured to the roof and covered with shingles.
If you have cracks in the chimney cap, you have 2 options. First you can remove and replace the cap with new materials. Coat the top surface of the cap with a commercial clear waterproofing agent. The second option is to have a copper cap fabricated to fit over the existing cap. It is best to first coat the existing cap with a sheet-applied membrane waterproofing, covering all exposed surfaces. The copper serves to protect the membrane.
If you have a masonry chimney, it is wise to coat all exposed masonry surfaces with a clear masonry waterproofing agent. This is applied in 2 separate coats with a garden sprayer set on low pressure and let the waterproofing run down the brick to assure adequate material is being installed. Let dry and re-apply. Make sure the waterproofing is the commercial quality and not the residential quality. You are wasting your time and money with the watered-down residential materials. Search for good waterproofing from waterproofing installer supply houses or go to brick supply vendors.
If flashing to your roof is a problem or flashing does not exist, you may want to consider hiring a competent roofer for this detailed job as it is extremely important that the flashing is installed beneath the shingles and into the masonry properly.