Preheat your grill or a grill pan over medium-high heat.
In a small bowl, mix together the garlic powder, onion powder, chili powder, cumin, salt, and black pepper. Rub this spice mixture evenly over both sides of the chicken breasts.
In a separate bowl, whisk together the lime juice and olive oil. Place the seasoned chicken in a shallow dish and pour the lime marinade over it. Let it marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
Remove the chicken from the marinade and discard the marinade. Grill the chicken for about 6-7 minutes on each side, or until the internal temperature reaches 165°F.
During the last minute of grilling, sprinkle the shredded Monterey Jack cheese on top of the chicken and close the grill lid to melt the cheese.
Once cooked, remove the chicken from the grill and let it rest for a few minutes. Top with chopped cilantro and sliced avocado. Serve with pico de gallo and lime wedges on the side.