Preheat a grill to medium-high heat for indirect grilling.
Place the dough circles on the hot side of the grill. Let cook for 1 minute, then flip with tongs, moving to a cooler spot on the grill (about medium heat) until the dough begins to pull away from the grill, about 1 minute. Remove to a platter or baking sheet.
In a large bowl, toss the shredded chicken with the Buffalo sauce. Divide the chicken mixture between the 2 grilled crusts and top with equal amounts of mozzarella and blue cheese crumbles. Put the pizzas back on the grill and grill until the cheese melts, just a minute or 2.
Sprinkle with chives and garnish with celery leaves. Cut into fourths and serve.