1) In a bowl, add in mustard, apricot preserves and ginger. Mix well.
2) Pour half of the above mixture into a second bowl.
3) Dip the chicken breasts in one of the bowls of marinade. Cover and refrigerate the bowl for at least 2 hours.
4) On a preheated grill, place the chicken breasts about 6 inches away from the source of heat.
5) Grill for at least 6 to 8 minutes on one side. When a meat thermometer inserted in the thickest part of the meat reads 170F, the chicken is done.
6) Arrange the chicken breasts on a serving plate.
7) Drizzle it with the remaining mustard-apricot sauce.