but I would first look at the flashing around the chimney. I would first get a few tubes of Butyl Rubber Caulking. Get on the roof and begin caulking around the flashing and the between the flashing and the chimney. Check on the top of the chimney stack and make sure that there are no cracks between the flue and the rock.
Then you might need a cricket installed on your roof if the water or slope is causing ponding around this area. A cricket is like a ships bow, it diverts water away and around the chimney before it gets there. Take a hose up with you and see if water does pond next to the chimney.
Then depending on how your chimney sits in relation to the fall of the roof line, you might check up from the chimney for leaks. Water travels a long way after the leak before it drops. If you have a stack or turbine up fall from the chimney this could be it also.
Look at your inner roof from the attic and see if there are any dark water runs up from the chimney that are just falling at the chimney to make you think its the chimney.