Cut acorn squash in half lengthwise and remove seeds. Place upside down in glass baking dish with 1/2 inch of water and cover with foil. Bake at 350 for 35-45 minutes.
In large saucepan, combine chicken stock plus 2 cups of water and bring to a boil. Add brown rice and return to boil.
Cover and reduce heat to medium. Cook for about 20 minutes.
Add chopped celery, onion and carrots and stir into the rice. Cook for another 20-30 minutes, or until rice is tender. If need be, add 1/2 - 1 cup of water to prevent from drying out. Once rice has cooked, add in the shredded chicken. Season with salt and pepper, to taste.
In a small bowl, combine softened butter or margarine with the apricot preserves. After squash has cooked for 35-45 minutes, remove from oven, flip over the squash (using a hot pad!) and spoon the butter/preserve mixture into the squash. Using a fork, poke a few holes into the squash flesh, so that when the butter/preserve mixture melts, it can get deep down into the squash! Return to oven and continue baking, uncovered, for 20-30 more minutes, or until squash flesh is tender all the way through.
Serve Chicken and Rice with Apricot Acorn Squash.