Would a large fishing net with a long handle fit? It's what I've used to get chickens out of trees, weird locations, and off roofs (when they were stuck). I guess maybe I'd say keep it dark, but I mean with a chimney that's pretty vague and a useless suggestion. How big is the fireplace (l,w,d), and also how big is the chimney(l,w,d). If It's a shorter chimney, I would try to scare it out, but that also depends on the size.
Here's how to get a normal bird out of a chimney
Look inside the fireplace to locate the bird. If the bird is in the chimney rather than the fireplace, open the fireplace damper.
Place a large box, open side up, inside the fireplace opening. Prop the box up on the fireplace grate or another box, if necessary, so there is only about an inch between the box opening and the top of the fireplace.
Pull the box back out slightly and turn on the flashlight, setting the light inside the box. Push the box back into place in the fireplace.
Silence external noises in the room, such as music or a TV, as well as conversational voices. Wait in the silence until the bird enters the box.
Slide the cardboard sheet gently over the box opening, trapping the bird inside. Gently remove the box from the fireplace, taking the box and bird outdoors. Remove the cardboard top from the box to set the bird free.
If the bird is already in the fireplace, close all doors leading to the room. If halls and entryways do not have doors, cover the openings with sheets held in place with thumbtacks. Open one window and screen or an exterior door, in case the bird gets into the room.
Open the fireplace screen or door slightly. Slowly toss a towel over the the bird to trap it. Grab the ends of the towel to trap the bird inside the towel. Carry the towel gently outdoors, releasing the bird.
Dim the lights in the room if the bird escapes the fireplace. Guide the bird toward the open window or door with the broom. If it's dark outside, turn on an exterior light so the bird can find the exit.
Obviously, with the damper not going in your favor, that might be TL;DR and useless. Good luck, I guess? If all goes well, you'll have one heck of a story.