Combine all of the marinade ingredients in a gallon Ziploc bag (if you’d like you can place them all in a blender first to help bring out the flavors). Add the chicken to the bag and seal. Use your hands to massage the chicken through the bag and make sure the breasts are evenly coated with marinade. Place the bag in your refrigerator and allow the chicken to marinate for 6-10 hours, turning the bag once or twice to make sure the chicken is evenly coated by the marinade.
Pre-heat your grill until hot (ours was set at a medium temperature). Remove the breasts from the marinade and sprinkle with a bit of salt to taste. Transfer the chicken breasts to the hot grill. Cook through, flipping as needed. Ours took 10-15 minutes to cook, but depending on your grill, cooking times may vary.
For the topping, combine the olive oil, rice vinegar, garlic powder, onion powder, dried basil, dried oregano, salt and black pepper and stir together until well combined. Add the tomatoes, cucumbers, olives, fresh basil, red onion and feta cheese and stir until well coated.
When the chicken breasts are finished cooking, divide the topping evenly over the breasts and serve.