In a large bowl, whisk together olive oil, lemon juice, minced garlic, oregano, salt, and pepper to create the marinade.
Reserve 2 tablespoons of the marinade in a separate small container for basting.
Toss the chicken cubes in the remaining marinade until evenly coated; cover and refrigerate for 60 minutes.
Preheat grill to medium-high heat, approximately 400°F (204°C), and lightly oil the grates.
Thread the marinated chicken, bell peppers, and red onion onto the skewers in an alternating sequence.
Place skewers on the grill and cook for 12 to 15 minutes, turning occasionally to ensure even browning.
Baste the kabobs with the reserved marinade during the final 5 minutes of cooking.
Verify the internal temperature of the chicken has reached 165°F (74°C) before removing from the grill.
Rest for 3 minutes before serving.