In a small bowl, whisk together the olive oil, lemon juice, salt, pepper, garlic powder, and onion powder. Place the chicken breasts in a shallow dish and pour the marinade over them, turning to coat both sides. Cover the dish and marinate the chicken in the refrigerator for at least 30 minutes, or up to 24 hours.
Preheat your oven to 400 degrees F.
Arrange the sliced bell peppers, onions, and cherry tomatoes on a large non-stick baking sheet. Drizzle with a bit of olive oil and sprinkle with salt and pepper. Roast in the oven for 15-20 minutes, or until the vegetables are tender and slightly caramelized, flipping halfway.
While the vegetables are roasting, add the chicken breasts in a large skillet. Cook them over medium-high heat for 4-6 minutes per side, or until it's cooked through and reaches an internal temperature of 165 degrees F. Alternatively, you can bake the chicken in the oven for 25-30 minutes, or until it's cooked through.
Assemble the mixed greens on a serving platter or individual plates. Top with the chicken and roasted vegetables. Serve with your choice of dressing on the side.