Even a pipe up thru a second floor room can work. Here's a house we were looking at before we bought our current place. 6400 sq.ft., very high-end restoration of a 1740's mill, so we ain't exactly talking trailer park, here.
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Unfortunately, I searched my collection of photos on this house, and could not find an actual photo of the pipe going thru the master bedroom. It was simply a brightly polished section of double or triple wall pipe, no chase, but nicely finished with floor and ceiling flanges. Probably gave off a little heat into the bedroom, when the stove was cranking.
This place was 4 stories, so it was one heck of a run of pipe! The soffets / gutters were 53 feet above the lawn, according to the people who had done the roof.