Chimney leaks are actually very common; and, in most cases, touching up the sealant around the flashing is all that’s really needed. But if the leak persists no matter what, it can simply be water migrating in through the masonry surface.
Both the bricks and mortar are very porous. In addition to causing water leaks inside, as the mortar absorbs the water, it expands. That is why you’ll often see cracking all along the mortar lines.
A good quality masonry sealer is the solution. It can be applied to the surface using a garden pump-up sprayer. The sealer keeps water from soaking into the pores, which effectively completely stops the leak.
It also protects the surface against dirt and stains, and even helps prevent that chalky white residue you see a lot of times on brick surfaces.