Toss chicken, 1 tablespoon hot sauce, oil, and salt together in a large bowl until evenly coated; cover and refrigerate for 30 minutes or up to 3 hours.

Position oven rack in top third of oven; preheat broiler. Line a large rimmed baking sheet with foil.

Arrange the marinated chicken pieces in a single layer on the prepared baking sheet, leaving space between each piece. Broil until lightly browned, about 7 minutes. Remove from oven; discard any excess liquid.

Meanwhile, combine butter, honey and the remaining 3 tablespoons hot sauce in a medium saucepan; bring to a simmer over medium heat. Cook, stirring occasionally, until thickened, 4 to 5 minutes. Remove from heat and stir in vinegar. Transfer 2 tablespoons of the hot sauce mixture to a small bowl. Add the cooked chicken to the saucepan; toss until evenly coated.

Arrange the chicken mixture in a single layer on the same baking sheet. Broil until glossy and browned in spots and an instant-read thermometer inserted into the thickest portion registers 165°F, 3 to 5 minutes. Remove from oven; brush with the reserved 2 tablespoons hot sauce mixture. Transfer to a platter. Serve with blue cheese (or ranch) dressing, carrots and celery.