Combine chutney, vinegar, oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
Brush 1/4 cup chutney mixture evenly over chicken; sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Place chicken on a broiler pan that has been coated with cooking spray. Broil 6 minutes on each side or until done.
Combine the remaining chutney mixture, greens, mango, and jicama; divide salad evenly among plates. Cut chicken into 1/2-inch-thick slices, and arrange over salad. Sprinkle with cilantro.