Position a rack in the center of the oven and heat the oven to 325°F.
Pat the chicken dry and season it all over with salt and pepper. Put the chicken breast side down on a roasting rack in a medium (9x13-inch or similar) roasting pan or flameproof baking dish. Tuck the wing tips behind the neck.
Roast the chicken for 30 minutes. Flip and continue roasting until an instant-read thermometer inserted in a thigh registers 165°F to 170°F, about 45 minutes more.
Transfer the chicken to a cutting board and let rest until cool enough to handle, about 30 minutes.
Pull off all of the meat, discarding the skin and reserving the bones; shred the meat into bite-size pieces, cover, and refrigerate.
Put the chicken bones in a 5- to 6-quart pot with the onion and celery trimmings. Add 8 cups of water and bring to a boil over high heat, skimming off any foam that rises to the surface. Lower the heat and simmer until flavorful and reduced to about 6cups of liquid, 35 to 50 minutes. Strain the broth and measure it; you will need 6cups, so add water if necessary.
Heat the oil in a 7- to 8-quart enameled cast-iron Dutch oven (or other heavy-duty pot) over medium heat. Add the chaurice and use a wooden spatula to break it into small pieces. Raise the heat to medium high and add the andouille, tasso, onion, celery, bell pepper, and Creole seasoning. Cook, stirring often, until the vegetables are browned, 15 to 20 minutes.
Add the rice and cook, stirring often, until translucent, 2 to 3 minutes. Add the shredded chicken, reserved broth, garlic, thyme, bay leaf, and 3/4 tsp. salt; bring to a boil. Cover, lower the heat to maintain a simmer, and cook, undisturbed, just until the rice is tender, 20 to 25 minutes. Check the rice for doneness in several places.
Remove the pot from the heat. Using a fork, gently fluff the scallions into the jambalaya. Cover and let stand for 10 minutes to let the flavors meld. Serve with hot sauce, if you like.