In a small bowl, whisk together the olive oil, lemon juice, minced garlic, salt, and black pepper. Stir in the diced onion.
Place the chicken breasts in a large resealable plastic bag or shallow dish. Pour the marinade over the chicken, making sure each piece is well coated.
Refrigerate for at least 4 hours, or overnight for the best flavor.
Preheat the grill to medium-high heat and lightly oil the grates if needed.
Remove the chicken from the marinade, allowing any excess to drip off. Discard the remaining marinade.
Grill the chicken for 8–10 minutes per side, or until the internal temperature reaches 165°F.
If desired, grill lemon halves for 2–3 minutes and serve alongside the chicken.