1. Heat a large skillet over medium-high heat. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add 1 tablespoon oil to pan; swirl to coat. Add chicken to pan; cook 3 minutes on each side or until done. Remove from pan; keep warm. Add 2 tablespoons vinegar and syrup to pan; bring to a boil. Cook 1 minute or until reduced to 3 tablespoons. Return chicken to pan; turn to coat with glaze.
2. Cut Brussels sprouts in half lengthwise; thinly slice crosswise. Place remaining 1 tablespoon oil, 1 tablespoon vinegar, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a large bowl; stir well with a whisk. Add Brussels sprouts, currants, and apple; toss to combine. Serve slaw with chicken.