Cut chicken into long strips about 1/2 inch thick. Place chicken in a resealable plastic bag set in a deep dish.
In a small bowl, combine vinegar, cooking oil, soy sauce, orange peel and juice, curry powder, chili powder and cumin. Pour marinade over chicken; seal bag. Marinate in the refrigerator for 2 to 6 hours, turning bag occasionally. Drain chicken, discarding marinade.
Soak wooden skewers in warm water for 1 hour before grilling; drain. With nonstick cooking spray, lightly grease wooden skewers. (Or use twelve 6- to 8-inch metal skewers.) On skewers thread chicken, accordion-style. Transfer skewers to a baking sheet or tray to transport to grill.
For charcoal, grill, grill skewers on the rack of an uncovered grill directly over medium coals for 8 to 10 minutes or until chicken is no longer pink (170 degrees F), turning to brown evenly. (For a gas grill, preheat grill. Reduce heat to medium. Place skewers on grill rack over heat. Cover; grill as above.) To serve, stir 1 cup of the Sweet Mango Chutney into the hot cooked rice. Spoon onto serving platter. Arrange chicken skewers over rice mixture. Spoon remaining chutney over the skewers. Makes 4 servings.