floor leveler in chimney

I have a weird question.... We have a brick dual ceramic flue chimney (maybe 1 ft x 3 ft) running up the side of our house. In the basement the footing for this chimney is less than two feet below ground (it does NOT go to the basement floor). The top has a cap. The part that is underground was brick, but two years ago I had a cement wall built around this underground brick, maybe 2 or three inches think, basically a foundation wall built around the underground portion of the chimney. I had this done because anytime we got a huge rainstorm (3+ inches in a day), the underground portion of the chimney would fill with water. This worked for over two years and many big storms until the storm we just got in New England. We got about 5 inches of rain in 24 hours. The chimney stayed dry until we hit the 4 inch mark in rain, then started to slowly fill with water. I pulled about 10 gallons from it using a wet vac. The outside is sloped away from the chimney and there no standing water. So my thoughts are:
Water must be coming up from bottom. My thought (and probably dead wrong), was to buy floor leveler and pour in a new base ("floor") inside the chimney cleanout maybe an inch or so thick? There can't be that much pressure pushing up as these cleanouts sit maybe 3-4 feet above the basement floor and no water is coming in through basement floor. Below is very crude diagram.
------------------------------------------------------------------------- basement ceiling | | | | ~~~~~~~~~~~~~~~~~~~~~~~~ ground level | | | | | xxxx xxxx | <---- this box is the chimney (x's are the two cleanout doors) | | ------------------------------------- <----- chimney footing
-------------------------------------------------------------------------- basement floor
I'm also going to price out having the entire undergorund portion of chimnet filled in with cement and clean out doors moved outside.
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On Fri, 12 Dec 2008 13:54:19 -0800 (PST), " snipped-for-privacy@aol.com"
...

I agree.
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We already have an interior french drain for the whole basement. This never takes on water, and the pump only runs about 2-3 storms a year (takes 4+ inches of rain in a day for the sump to even show any water). How would I install and interior french drain in the chimney base? Dumb question but how would I (or contrater) get in there? The spot is a 2x3 foot cavity that is about 1-2 feet below ground.
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Is there a chimney cap to keep the rain from pouring sown the chimney?
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OP says theres is in openinmg post
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Oops. Missed that.
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