Whisk oil, lemon juice, vinegar, garlic, cumin, oregano, thyme, salt, and black pepper (to taste) in a large glass or ceramic bowl. Cover and marinate in refrigerator for at least two hours.

Soak wooden skewers for about 30 minutes before use.

Preheat outdoor grill for medium-high heat and lightly oil grate.

Remove chicken from marinade and shake off excess liquid. Discard remaining marinade. Alternate chicken with pieces of bell pepper, onion, cherry tomatoes, and mushrooms onto the skewer

Cook the skewers on grill, turning frequently until nicely browned on all sides. About 10 minutes.