In a large bowl, whisk together olive oil, lime juice, garlic, chili powder, cumin, paprika, salt, black pepper, and cayenne pepper. Add the chicken breasts and coat well. Cover and marinate in the refrigerator for at least 30 minutes, or up to 4 hours for more flavor.
Preheat the grill to medium-high heat. Remove the chicken from the marinade and discard the marinade. Grill the chicken for 6-7 minutes per side, or until the internal temperature reaches 165°F.
While the chicken is grilling, prepare the avocado salsa. In a medium bowl, combine diced avocados, cherry tomatoes, red onion, cilantro, lime juice, salt, and pepper. Gently mix to combine.
Once the chicken is cooked, let it rest for 5 minutes before slicing. Serve the chicken topped with avocado salsa.