Heat oil in heavy small saucepan over medium heat. Add shallot and saute until beginning to soften, about 1 minute. Add maple syrup and mustard and simmer until mixture thickens and bubbles, stirring occasionally, about 2 minutes. (Glaze can be prepared 1 day ahead. Cover and refrigerate.)
Preheat broiler. Season chicken with salt and pepper. Place chicken on small broilerproof pan. Brush with glaze. Broil chicken 5 minutes. Turn chicken over; brush with glaze. Broil until chicken is golden brown and cooked through, about 8 minutes. Transfer chicken to plates. Bring any remaining glaze just to boil and pour over chicken. Serve hot.