Preheat your grill to medium-high heat.
In a mixing bowl, combine the olive oil, balsamic vinegar, garlic powder, dried oregano, salt, and pepper. Mix well.
Add the chicken breasts to the marinade, ensuring they are well-coated. Let them marinate for at least 10 minutes.
While the chicken is marinating, prepare the vegetables by tossing them with a little olive oil, salt, and pepper in a separate bowl.
Once the grill is ready, place the marinated chicken breasts on the grill. Cook for about 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C).
After flipping the chicken, add the vegetables to the grill. Grill for about 5-7 minutes, turning occasionally, until they are tender and slightly charred.
Remove the chicken and vegetables from the grill. Let the chicken rest for a few minutes before slicing.
Serve the grilled chicken alongside the grilled vegetables on a platter.