In a small bowl, whisk together the lime juice, olive oil, cilantro, cumin, and salt.
Place the chicken in a resealable bag or shallow dish and pour the marinade over it. Refrigerate for at least 15 minutes or up to 2 hours.
Preheat a grill or grill pan to medium-high heat (about 400°F / 200°C).
Grill the Cilantro Lime Chicken for 4–6 minutes per side, or until the internal temperature reaches 165°F (74°C).
Remove the chicken from the grill and let it rest for 5 minutes.
Meanwhile, prepare the avocado salsa by gently combining the diced avocados, cilantro, lime juice, apple cider vinegar, red pepper flakes, garlic, and salt.
Spoon the avocado salsa generously over the grilled chicken and serve immediately.