Preheat oven to 425°F. Line a large baking sheet with parchment paper.
Place cauliflower and garlic in a food processor; process until finely chopped. Transfer to a microwave-safe bowl and microwave on High for 3 minutes. Let cool slightly. Stir in eggs, mozzarella, carrot, 2 tablespoons chives and salt. Spread the mixture into a 12-inch circle, 1/4 inch thick, on the prepared baking sheet.
Bake the cauliflower crust until brown and crispy around the edges, 35 to 40 minutes.
Combine chicken, 1 tablespoon hot sauce, vinegar and cayenne in a small bowl. Remove the crust from the oven and top with the chicken and blue cheese. Return to the oven and bake until the chicken is warm and the cheese is starting to melt, about 5 minutes more. Top with celery and the remaining 1 tablespoon each chives and hot sauce.