Heat oven to 400°F. Rub chicken with oil, salt and pepper and roast in a small baking dish for 40 to 50 minutes until the thickest parts reach 165°F without the thermometer touching bone.
Rest chicken for 10 minutes. Remove every bone and any firm connective tissue, then tear the meat into broad bite-sized pieces.
Warm hot sauce and butter together in a small saucepan just until the butter melts. Toss the warm chicken with the sauce until coated.
Stir crème fraîche, blue cheese and lemon juice in a bowl. Fold in celery and carrot ribbons so the vegetables are lightly dressed rather than swimming in sauce.
Split the rolls and toast only their cut faces under the broiler for 1 to 2 minutes. Divide Buffalo chicken along the bottoms and add the cold vegetable mixture.
Close gently and cut across the middle. Serve one sub per person immediately, leaving any loose sauce in the chicken bowl.