In a mixing bowl, combine lime juice, olive oil, minced garlic, chili powder, cumin, salt, black pepper, and cayenne pepper (if using) to create a marinade for the chicken.
Place the chicken breasts in a large resealable bag or dish and pour the marinade over them. Seal or cover and refrigerate for at least 30 minutes, or up to 2 hours for best flavor.
While the chicken marinates, prepare the avocado salsa. In a separate mixing bowl, combine diced avocados, cherry tomatoes, red onion, cilantro, lime juice, salt, and pepper. Gently toss to combine and set aside.
Preheat your grill or skillet over medium-high heat. Remove the chicken from the marinade and discard the marinade.
Grill or cook the chicken for about 6-8 minutes on each side, or until the internal temperature reaches 165°F (75°C) and the chicken is nicely browned.
Once cooked, allow the chicken to rest for a few minutes before slicing.
Serve the sliced Fiesta Lime Chicken topped with the fresh Avocado Salsa.