Heat grill to medium-high.
Combine garlic, 1 tablespoon olive oil, chipotle, honey, and 1/2 teaspoon salt in a small bowl. Set aside.
Rub chicken breasts all over with olive oil and generously season with salt and pepper. Cook chicken breasts on the grill until cooked through, about 4-5 minutes per side. Remove and shred chicken with two forks. Toss shredded chicken with 2 tablespoons of the chipotle mixture.
Lightly brush crusts with remaining teaspoon of oil on both sides. Divide remaining chipotle mixture between the crusts and spread in a thin layer. Top with chicken, bell pepper, and cheese.
Carefully transfer pizzas to the grill and cook until crusts are golden and cheese is melted, about 4 minutes. Watch carefully and move around as needed to prevent crusts from burning.
Enjoy with a green salad tossed with cherry tomatoes, scallions, and sliced avocado.