Interesting. If I could get it down below the roof, I'd take it down the rest of the way!
In my case, the mortar had failed in the top part of the chimney. I could just tap the bricks with a hammer and they'd pop loose. As long as I was above the roof line I could heave them into the yard. Once I got below the roof, I had to start hauling them to a gable opening, which was a lot more work, and the mortar got more solid.
I considered removing it entirely, but I wasn't sure how structural it was. I know that portions of it serve as a foundation pier. Also, it was a lot more massive than yours -- about 30" square.
Yours I'd wrap in drywall and be done -- at least until you remove it entirely. Most of ours is in the corner of a walk in closet now.