Preheat oven to broil with rack about 6 inches from heat source. Stir together cumin, chili powder, paprika, salt, and black pepper in a small bowl. Line a rimmed baking sheet with aluminum foil. Toss together chicken, bell peppers, onion, oil, and cumin mixture on prepared baking sheet; spread in an even layer.
Broil in preheated oven, undisturbed, until chicken is cooked through and vegetables are charred and beginning to soften, 10 to 12 minutes. Remove from oven; add lime juice to mixture, and stir to coat. Serve with warm tortillas and desired toppings.
