A word of advice. A fireplace is a heat LOSER. They have a negative effect on heat retention in a home. My suggestion is a woodstove insert in that fireplace!

What kind of chimney do you have? Is it a metal chimney? If so, you might have a "zero clearance" fireplace. We had two in a previous house and the "box", or "chase" was completely sealed, top and bottom. Insulated? no, but the sides were wood as was the bottom. The top was tin flashing. And the home was warm.

But we then put in a woodburning insert into the fireplace. And the difference was amazing. We used less than half the wood, and we were toasty! Your fireplace has an 8" chimney, and woodstoves have a 6" chimney. They just ran a liner up the chimney and insulated it with "Kaowool", a ceramic fiber insulation. If you do something like this, you won't need to insulate the chase itself as the stovepipe will keep the chase warm. But you DO need to seal off the chase. And that will eliminate a LOT of the cold air.

PS. The money you spend on a wood burning insert will pay back over the long run in time, energy and wood savings. And nowhere near the pollution of a fireplace.