In a large bowl or zipper freezer bag, add the olive oil, lemon juice, balsamic, Dijon, and seasonings. Whisk well to combine. Remove ¼ cup and set aside in a separate bowl, then add in chicken breast and toss to coat. Cover and chill, marinating for at least 30 minutes and up to 8 hours.
When ready to cook, preheat oven to 400°F. Line a baking sheet with parchment or foil, lightly spraying it with cooking spray.
Prepare the vegetables, then place them in the bowl with the reserved marinade, tossing well to coat.
Thread wooden or metal skewers with alternating pieces of marinated chicken, peppers, mushrooms, and onion.
Bake for 15-20 minutes, flipping once, until the chicken is cooked through to 160°F on an instant read thermometer.
Set oven broiler to high and broil the skewers for 1-2 minutes on both sides until lightly charred, watching closely so they don’t burn. Allow skewers to rest for 5 minutes before serving.