Combine first 6 ingredients in a bowl; stir well with a whisk. Set aside.
Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add chicken; cook 4 minutes on each side or until done. Cut the chicken into 1/8-inch-thick slices.
Cut off the raised portion of the main vein of each lettuce leaf. Divide chicken evenly among lettuce leaves; top with carrot, jicama, cucumber, bean sprouts, and cabbage, dividing evenly. Roll up, and secure with a pick. Serve with sauce.