Mix oil, vinegar, Seasoning, mustard and oregano in small bowl until well blended. Place chicken in large resealable plastic bag or glass dish. Pour 1/2 of the dressing over chicken; turn to coat well. Reserve remaining dressing for the salad.
Refrigerate chicken 30 minutes or longer for extra flavor. Remove chicken from marinade. Discard any remaining marinade.
Grill over medium heat 5 to 7 minutes per side or until chicken is cooked through. Slice chicken into thin slices. Toss salad greens and tomato in large bowl. Top with chicken. Whisk reserved dressing. Drizzle over salad.