Preheat oven to 375 °. Combine oil, soy sauce, honey, vinegar, thyme, paprika, cayenne pepper, allspice and pepper in a shallow baking dish; mix well.

Pierce both sides of each chicken breast with fork. Place in baking dish; turn chicken several times using prongs.

Bake chicken, basting several times with sauce, for 30 minutes.

Spoon rice onto a serving platter. Arrange chicken over rice. Drizzle a small amount of sauce over chicken. Serve remaining sauce on the side.