Pat the chicken breast dry with paper towels. Melt 1 tbsp of the butter in a stock pot over medium heat. Season the chicken with salt and pepper and brown, about 5 minutes per side. Reduce heat to low and cover the pot. Continue to cook until the chicken is cooked through, (an internal temperature of 165F), about 5 minutes more. Transfer the chicken to a cutting board and allow to rest 10 minutes. Cut into bite-sized pieces (I like mine small!)
Melt the remaining butter in the stock pot over medium heat. Add the onion, celery, carrots, garlic, and red pepper, and season with 1/4 tsp salt. Sweat until the onions are translucent, about 15 minutes. Add the wine and thyme and simmer 10 minutes.
Increase the heat to medium-high, add the chicken stock, and bring to a low boil. Taste for salt. Add the noodles and cook until tender. Stir in the chicken just before serving.