In a bowl, whisk together the olive oil, lime juice, garlic, brown sugar, cumin, salt, black pepper, and cayenne pepper until well combined.
Place the chicken breasts in a zip-top bag or shallow dish and pour the marinade over the chicken. Seal and refrigerate for at least 1 hour, or overnight for best flavor.
Preheat the grill to medium-high heat and lightly oil the grates.
Remove the chicken from the marinade and discard any remaining marinade.
Grill the chicken for 6 to 7 minutes per side, or until the internal temperature reaches 165°F (74°C).
Remove from the grill and let rest for 5 minutes before slicing and serving.