Preheat the broiler. Season the chicken pieces generously with salt and pepper.
In a small saucepan, melt the butter. Whisk in the hot pepper sauce and vinegar. On a broiler pan or baking sheet, toss the chicken strips with half the hot sauce mixture. Broil the chicken, turning once, until tender and just golden, 7 to 9 minutes. Remove from the oven and pour the remaining sauce over the chicken; set aside.
Meanwhile, in a bowl, stir together the mayonnaise, sour cream and Worcestershire sauce. Stir in the blue cheese.
To serve, divide the blue cheese dressing among 4 martini glasses. Stand the chicken strips and celery stalks upright in the dressing.