How would you frame this chimney chase?
I did something similar to replace a chimney that was damaged in an earthquake and had to be replaced. Instead of building a new chimney I replace the old removed flue with 10 inch inside diameter stainless steel triple wall insulated stack piping inside of a tall chase. I built the chase much larger than your proposed 12&quot;x12&quot; size. My chase was, as near as I recall as it was about 26 years ago, about 30 inches parallel to the wall and 16 inches out from the wall. My structure was 16 feet in height so I framed it in two ~8 foot sections with conventional double plate between the vertical sections of studs.
I see no need to sheet out the sides with 3/4 inch material. Whatever sheathing is currently on your house should be a guide whether that be 1/2&quot; or 5/8&quot; plywood or OSB. In my case I used 1/2&quot; plywood because it was a good base for the stucco exterior that was applied afterward.
So the crux of my suggestion is that you go a bit larger than your 12x12 size. It will be stronger. It will also be better looking in my opinion than the tall skinny box.