In a small bowl, combine the olive oil, lemon juice, minced garlic, salt, black pepper, and dried oregano to create the marinade.
Place the chicken breast in a resealable bag or shallow dish and pour the marinade over it. Let it marinate for at least 30 minutes in the refrigerator.
Preheat your grill to medium-high heat. Grill the chicken breast for about 6-7 minutes per side, or until the interior reaches a safe cooked temperature and has attractive grill marks.
While the chicken is grilling, preheat your oven to 425°F for the broccoli. Toss the broccoli with a little olive oil, salt, and pepper, and spread onto a baking sheet. Roast in the oven for about 15 minutes until tender and slightly crispy.
Prepare the quinoa according to package instructions if not pre-cooked.
To assemble, place a portion of quinoa on the plate, top with sliced grilled chicken breast, and serve with a side of roasted broccoli. Optionally, drizzle any remaining marinade (boiled for safety if reused) over the chicken for extra flavor.