Right - the outlet won't actually go into the masonry. The chimney is surrounded by a regular 2x4-framed finished wall on all sides (except for the fire box opening on the living room side).
The chimney itself (not the wall) tapers considerably from its foundation in the basement to where it exits the roof. The wall was framed with the 2x4's in the usual orientation (not the flat way), meaning there is sufficient clearance for a normal-deepth box. Due to the taper of the chimney, the further your get from the floor, the more depth there is between the face of the wallboard and the actual bricks of the chimney. At countertop height, there is plenty of room.
I was planning to use flexible metal conduit and fish-in a flush-mount box. Why flexi-conduit over romex? Mainly because I have those materials on hand.
I will have access to the stud cavities in that wall from either above (attic) or below (basement).
Thank you everyone for your prompt replies. I really appreciate your opinions and advice.