The old stucco might be responsible for leaks and the base / foundation of the chimney
could have something to do with it as well.
Cinderblocks absorb moisture unless sealed and their mortar joints deteriorate over time, especially under the ground. Even if there was some moisture retarder applied to the surface of the blocks below the ground level it might have deteriorated or there could be a crack that permits water seepage into the crawlspace.
For testing you could put a tarp over the chimney walls to eliminate stucco-leakage possibility and monitor the crawlspace for leaks. If there’s still some seepage you’d have to dig around the base of the chimney / all the way to the bottom, clean the cinderblock surface and apply tar or other waterproofing layer. Mortar joints and / or any cracks may need to be replaced as well.
However, if the stucco is already crumbling, even if this is not directly responsible for water penetration, it will cause further deterioration of the mortar joints underneath.
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