Preheat your grill or grill pan over medium-high heat. In a small bowl, mix together olive oil, garlic powder, onion powder, oregano, paprika, salt, and pepper. Rub this mixture all over the chicken breasts.
Grill the chicken for about 6-7 minutes on each side, or until the internal temperature reaches 165°F. Remove from the grill and let it rest for 5 minutes before slicing.
In a large bowl, combine the cooked quinoa, cherry tomatoes, cucumber, olives, feta cheese, and parsley. Drizzle with lemon juice and toss gently to combine.
Slice the grilled chicken and serve it on top of the quinoa salad mixture. Drizzle with additional olive oil or lemon juice if desired.