Microwave the chocolate in a microwavable bowl on high for 2 minutes, stirring after 1 minute. Stir until completely melted.
Dip the apricots halfway into the chocolate. Let the excess chocolate drip off. Place the apricots onto waxed paper. Sprinkle the pistachios over the chocolate-covered portions of the apricots. Place in the refrigerator until the chocolate is set.