In a bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, dried oregano, salt, and black pepper.
Add the chicken breasts to the bowl and toss to coat with the marinade. Let the chicken marinate for at least 10 minutes (or up to 30 minutes for more flavor).
Meanwhile, rinse the quinoa and place it in a medium saucepan with 2 cups of water. Bring to a boil, then reduce heat, cover, and simmer until the quinoa is tender and the water is absorbed, about 15 minutes. Fluff with a fork and set aside.
Heat a grill pan or skillet over medium-high heat. Cook the marinated chicken breasts for about 6–7 minutes per side, until cooked through and no longer pink in the center. The internal temperature should reach 165°F (74°C).
Remove the chicken from heat and let it rest for a few minutes, then slice it into bite-sized pieces.
In a large bowl or individual serving bowls, divide the cooked quinoa.
Top the quinoa with sliced chicken, cherry tomatoes, diced cucumber, kalamata olives, and crumbled feta.
Sprinkle with chopped parsley and serve with lemon wedges on the side.