Water coming into a chimney will be absorbed into the bricks. More water coming into the chimney will then continue to soak further down creating a very humid condition inside of the chimney. This can stimulate the growth of mold that will smell musty or like mildew, called "Chimney Breath". The best solution is twofold: Have your chimney cleaned early in the spring to make the humid summer days less odiferous; Have a chimney cap installed that will stop the majority of the rain coming into the chimney. Without a chimney cap, there is no real cure for this problem other than fireplace deodorants that can eliminate or "cover up" the odor.