I have removed the siding and sheathing from the bottom of a cantilevered exterior chase for some renovation work. There is no insulation in there besides foil faced foam board sheathing, which I am replacing with 7/16 OSB sheathing.

The fireplace is a Heatilator FP36 from 1986. The label says: “Install chimney at 2” minimum to enclosure. Fireplace bottom, sides and back may be adjacent to enclosure.”

What should I insulate underneath the fireplace and the walls of the chase with? Unfaced batts? What about a a vapor barrier?

The fireplace is raised up off the subfloor, so I need to insulate the floor joists underneath where the stick out from the basement, and also this area where it is raised up: