MAKE-AHEAD:Chicken and peppers can be grilled and refrigerated separately in covered containers up to 1 day ahead. Warm gently on stove top or in microwave before serving.
Arrange chicken snugly in a baking dish. Whisk together 2 tablespoons of the oil, 2 tablespoons of fresh lime juice, garlic, salt, and black pepper in a small bowl; pour marinade over chicken and turn to coat. Cover and refrigerate for 30 minutes.
Heat a grill or grill pan to medium-high. Remove chicken from marinade and grill until cooked through, about 5 minutes per side. Discard remaining marinade. Transfer chicken to a plate, cover loosely, and keep warm.
Brush bell peppers with remaining 1 teaspoon oil and grill until softened and lightly charred, about 5 minutes. Transfer to a plate, cover loosely, and keep warm. Grill tortillas, in batches, to make pliable, about 30 seconds per side. Cut each tortilla into quarters.
Makes 8 servings. Each serving is 3 piece servings.
Cut chicken crosswise on the bias to make 24 thin slices; cut slices in half, if desired. Arrange tortilla pieces on a serving platter. Spoon 1/2 teaspoon sour cream onto each tortilla quarter. Divide chicken, peppers, and cilantro among tortillas. Serve warm with 8 lime wedges.