Melt butter in a large pot or Dutch oven over medium-high heat. Season chicken pieces with salt and pepper, then add to the pot. Cook for 5-6 minutes until chicken is browned and cooked through. Remove chicken and set aside.
In the same pot, add diced onion and celery. Sauté for 3-4 minutes until softened. Add garlic and cook for another minute.
Add the pasta, chicken broth, and buffalo sauce to the pot. Stir well and bring to a boil.
Reduce heat to medium and simmer for 12-14 minutes, stirring frequently, until pasta is tender and most of the liquid has been absorbed.
Return the cooked chicken to the pot. Stir in heavy cream and cheddar cheese until the cheese melts and the sauce becomes creamy.
Top with crumbled blue cheese and sliced green onions. Serve hot with extra buffalo sauce on the side for those who like it extra spicy!