In a medium bowl, whisk together lime juice, olive oil, minced garlic, cumin, chili powder, salt, black pepper, and cayenne pepper (if using).
Place the chicken breasts in a resealable plastic bag or shallow dish and pour the marinade over the chicken. Seal the bag or cover the dish and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
While the chicken is marinating, prepare the avocado salsa. In a separate bowl, combine diced avocado, tomato, red onion, cilantro, and season with salt and pepper to taste. Gently toss to combine and set aside.
Preheat the grill to medium-high heat. Remove the chicken from the marinade and discard the marinade.
Grill the chicken for 6-7 minutes on each side, or until the internal temperature reaches 165°F and the chicken is cooked through.
Remove the chicken from the grill and let it rest for 5 minutes before slicing.
Serve the sliced chicken topped with avocado salsa.