Preheat the grill to medium-high heat (about 400°F).
In a small bowl, combine 1 tablespoon olive oil, garlic powder, smoked paprika, dried oregano, salt, and black pepper to make the chicken marinade.
Brush both sides of each chicken breast with the marinade mixture.
In a large bowl, toss zucchini, red bell pepper, yellow bell pepper, and red onion with the remaining 1 tablespoon olive oil, dried thyme, salt, and pepper.
Place the chicken breasts on the grill and cook for 6-7 minutes on one side without moving, until grill marks form.
Flip the chicken breasts and grill for another 6-7 minutes, or until the internal temperature reaches 165°F and the chicken is cooked through.
While the chicken is grilling, place the vegetables in a grill basket or on a grill-safe tray and grill for about 10-12 minutes, turning occasionally, until tender and lightly charred.
In a large bowl, combine mixed salad greens, cucumber slices, and cherry tomatoes.
In a small bowl, whisk together balsamic vinegar and extra virgin olive oil to make the salad dressing.
Drizzle the dressing over the salad and toss gently to combine.
Remove the chicken and vegetables from the grill and let the chicken rest for 5 minutes.
Serve each grilled chicken breast with a portion of grilled vegetables and a side of fresh garden salad.