Preheat your grill to medium-high heat.
In a small bowl, whisk together olive oil, lime juice, minced garlic, chili powder, cumin, salt, black pepper, and cayenne pepper (if using).
Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour half of the marinade over the chicken, ensuring it is well coated. Reserve the other half for the avocados.
Marinate the chicken in the refrigerator for at least 30 minutes, or up to 2 hours for more flavor.
While the chicken is marinating, prepare the avocados. Brush the cut sides of the avocado halves with the reserved marinade.
Once the chicken has marinated, remove it from the refrigerator. Grill the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F.
During the last 2-3 minutes of grilling, place the avocado halves cut-side down on the grill. Grill until they have nice grill marks and are slightly softened, about 2-3 minutes.
Remove the chicken and avocados from the grill. Let the chicken rest for a few minutes before slicing.
Serve the sliced chicken topped with grilled avocado halves, garnished with fresh cilantro and lime wedges.