Stir together oil and next 4 ingredients in a large bowl. Add chicken, tossing to coat. Arrange chicken in a single layer on a wire rack in an aluminum foil-lined jelly-roll pan.
Bake at 450° for 30 to 35 minutes.
Combine mustard, lemon juice, and oregano in a large bowl. Remove pan from oven, and carefully add hot chicken to mustard mixture. Toss to coat. Drain and discard any accumulated fat from pan. Place mustard-coated chicken in a single layer on rack in jelly-roll pan.
Bake at 450° for 8 to 10 more minutes or until done.