Combine first 7 ingredients. Cover and chill. Place chicken in a shallow dish. Combine 2 tablespoons lime juice, soy sauce, and garlic. Pour over chicken. Cover and marinate in refrigerator 1 hour.
Soak mesquite chips in water 30 minutes; drain.
Remove chicken from marinade, reserving marinade. Thread chicken onto 2 (10-inch) skewers. Place chips directly on medium-hot coals (350° to 400°). Coat grill rack with cooking spray; place rack on grill. Place chicken on rack; grill, covered, 6 to 8 minutes or until chicken is done, turning occasionally and basting with reserved marinade.
To serve, spoon tomato mixture onto a serving plate; place chicken kabobs over tomato mixture.