The breakdown of chimneys and other masonry walls are an indication of roof replacement. If water is coming in along the chimney wall or masonry wall it is either because the counterflashing is failing or the masonry itself is absorbing water.
This picture shows that the caulking has deteriorated to the point that it is actually missing and water can get behind the metal and enter your home. Deterioration can also occur on the concrete chimney cap which allows moisture to enter as well as weaken and destroy the entire masonry structure. By checking the caulking and maintaining the chimney with masonry sealant, the cost of repair or replacement are avoided.