Chimney box repair

Planning on replacing the rotted wood trim on my chimney box (replaced the siding about three years ago with Hardy board cement siding). I'll need to pull the chimney cap and top plate to access the upper trim work (Didn't have to do this a few years ago).
I can see how the cap comes off as it looks like I just pry open the banded clamp at the base and lift off. Top plate looks like it just lifts off the stove-pipe, as well.
Question: Are these stovepipes usually a single unit from the fireplace to the chimney cap? Guess what I'm asking is . . what's the probability of the pipe inadvertantly coming apart somewhere in the middle, or worse yet at the fireplace, where access is severely limited???
Thanks,
Phil
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I don't want to sound dumb, but what is a chimney box?
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If you are talking the stainless steel double pipe the ones I have seen are twist lock so as long as you pry without twisting the lower sections should stay together.
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OK, I'll try not to twist. That would make sense to have them fit that way.
Not sure of the "official" name, but I'm referring to the wooden framed box structure that fits around a chimney pipe coming through the roof to give it a chimney appearance. Mine's about 3' X 5', with siding on all four sides and trimmed out with 1X4s around the top and corners, a heavy steel plate fitted over the top with a chimney cap on top.
Thanks for the inputs.
Phil
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Gotcha.
I have no idea what the proper name for it is. I may BE "chimney box".
Just say "That part of the house that surronds the chimney"
;-]
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wrote

Chimney Chase?
Bob
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wrote

Ya know: I think that IS what it's called. I have a real masonary chimney on the house I'm in now, but on my last house (where I had an oil-fired furnace), it was just double-walled "all fuel" pipe through the roof and then (for looks) a metal box painted with bricks to LOOK like a brick chimney.
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