It sounds to me like you need a chimney cap or you need to have your chimney bricks pointed.  The other problem could be the roof flashing that goes around the base of the chimney, it may need to be re-sealed.  You need to call someone that does brick pointing, but make sure that they have experience with chimney work. You could also call a roofer and ask them to give you a visual inspection of the roof.  When they go up on the roof, they will look for any signs of the cause.  If it's not the roof they should be able to see if the problem is with the chimney.  Good luck.