Set a large 6+ quart saucepot over medium heat. Add butter. Once melted, stir in the kielbasa sausage. Brown the sausage for 2 minutes.
Then stir in the diced onions, diced carrots, diced celery, garlic, dried thyme, and crushed red pepper. Sauté for 3-5 minutes.
Meanwhile, liberally salt and pepper the chicken pieces. Once the veggies have softened, push them to the sides and move the chicken pieces to the bottom of the pot, skin-side-down. Brown for 2-3 minutes.
Flip the chicken over and add the broth, 1 teaspoon salt, and ½ teaspoon black pepper.
Cover and simmer on medium to medium-low for 25 minutes. Remove the chicken pieces with tongs. Discard the skins and bones. Break the chicken meat up a little bit, then stir the chicken chunks back into the broth.
Use a wooden spoon to clear any stuck-on debris from the bottom of the pot. Stir in the rice. Then cover and cook the rice for 15 minutes.
Once the rice is soft and you see vent holes in the top layer of rice, turn off the heat.
Stir in the frozen peas to warm. Taste, then add salt and pepper as needed. Serve with hot sauce on the side.
