First off, we need to deal with both the potential of a leaking chimney and a leaking basement, because they are clearly working together to create this issue.First, examine the exterior of the chimney, looking for cracks and gaps where water can get through. Secondly, look at the top of the chimney. In fact, it's is very common to for rain to get in through a damaged chimney crown - which is the concrete surface that goes between the clay flue and the exterior of the brick edge. If you don't have a chimney cap, you should install one. That's advisable because it slows down the amount of rain water getting into the chimney.Next, look at the drainage conditions around your house. Soil around the foundation of the whole house, but especially where chimney is, should slope away from the foundation. Gutters should be clean and free flowing with downspouts directed away at at least 4-6 feet from house. All those actions will reduce or at least slow the water coming in. As a final step, you may want to apply a masonry sealer around the the exterior of the chimney. Masonry sealers are specially designed to be vapor permeable. That means while the sealer will keep most of the water out, it will still allow moisture to evaporate out of the brick exterior in winter - so the bricks won't freeze and break.Good luck and let us know how it works out!