1. Preheat grill to 350º to 400º (medium-high) heat. Whisk together first 6 ingredients in a small bowl. Pour half of olive oil mixture into a shallow bowl or zip-top plastic freezer bag; add chicken, turning to coat. Cover or seal, and let stand 10 minutes. Pour remaining olive oil mixture into another bowl or freezer bag; add bell pepper, tomatoes, and mushrooms, and toss to coat; cover or seal, and let stand 10 minutes.
2. Remove chicken and vegetables from marinade, discarding marinade. Thread chicken onto 8 skewers. Thread vegetables alternately onto remaining 8 skewers.
3. Grill kabobs, covered with grill lid, 10 to 12 minutes or until chicken is done and vegetables are tender, turning occasionally. Remove kabobs from grill. Let stand 5 minutes before serving.