In a non-reactive bowl, whisk 0.25 cup lime juice, olive oil, 0.33 cup cilantro, minced garlic, cumin, salt, and pepper to create a marinade emmulsion.
Place chicken breasts in the marinade, ensuring full surface contact, and refrigerate for 15 to 30 minutes to allow acid penetration.
Preheat a cast-iron skillet or grill to 400 degrees Fahrenheit (204 degrees Celsius).
Remove chicken from marinade and sear for approximately 6 to 7 minutes per side until the internal temperature reaches a safe 165 degrees Fahrenheit (74 degrees Celsius).
While chicken cooks, combine diced avocados, brunoise red onion, 1 tablespoon lime juice, and remaining cilantro in a chilled bowl; toss gently to avoid oxidizing or crushing the avocado structure.
Transfer cooked chicken to a resting board for 5 minutes to allow muscle fibers to relax and redistribute juices.
Slice chicken against the grain if desired and top with a 0.5 cup portion of avocado salsa before immediate service.