This is unlikely going to cause enough water to get in to cause a leak. The only other possiblity is the flashing was not woven into the shingles properly, and the water is leaking through the shingles. Is the water leak on the uphill side or downhill side of the chimney? It sounded like it is on the downhill side. If it is on the uphill side, is there a gable on the roof coming up to the chimney. There are a lot of chimnies out there that do not have this. This allows water to run down the roof and run right up against the chimney. The only thing that keeps the water out of the house is flashing. There should be a gabled roof that comes up the chimney so that all the water is directed away from the chimney.