Melt butter in a large pot or Dutch oven over medium-high; season chicken with salt and pepper and cook 5-6 minutes until browned and cooked through. Set aside.
Sauté onion and celery in same pot 3-4 minutes until softened; cook garlic another minute.
Stir in pasta, broth, and buffalo sauce; bring to a boil.
Reduce heat to medium; simmer 12-14 minutes, stirring frequently, until pasta is tender and most liquid absorbed.
Return chicken; stir in cream and cheddar until cheese melts and sauce is creamy.
Top with blue cheese and green onions; serve hot with extra buffalo sauce for more heat.