Combine the chicken breasts and 1/2 cup of the Mexican Style Cilantro Lime Vinaigrette in a resealable plastic bag. Let marinate at room temperature for 15 minutes.
Meanwhile, cook the bacon in a large skillet over medium heat until crisp, about 5 minutes per side. Drain on paper towels.
Preheat an outdoor grill or grill pan to medium-high heat.
Oil the grills grate or grill pan. Remove the chicken from the marinade. Sprinkle with salt and pepper. Grill the chicken, turning once, until cooked through, about 4 minutes per side, depending on thickness.
Spread the mayonnaise on the cut surfaces of the rolls. Slice the chicken and add to the rolls. Break the bacon in half and place on top of the chicken. Top with avocado and tomato slices, cilantro leaves and radishes. Drizzle each sandwich with 1 tablespoon of the remaining vinaigrette. Press the tops on the sandwiches.
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