To make marinade: In large bowl, whisk olive oil, vinegar, soy sauce, lemon juice, brown sugar and garlic. Season with salt and pepper, to taste.
To make kebabs: In bowl, toss chicken, bell peppers, zucchini, squash and red onion with marinade. Cover and refrigerate 1-8 hours.
Soak wooden skewers in cold water at least 30 minutes to prevent burning. Preheat grill to medium-high heat.
Thread chicken pieces and vegetables onto skewers, alternating ingredients. Cook 5-7 minutes on each side, or until chicken is cooked through.
Sprinkle with parsley and serve.