Line a small baking sheet with waxed paper or parchment.
In a medium microwave safe bowl, place the chocolate pieces. Microwave on high power for 1 to 1½ minutes, stopping every 15 seconds to stir until most, but not all, of the chocolate is melted. Remove from microwave and stir the chocolate continuously until it is smooth and completely melted.
Dip the dried apricots into melted chocolate, coating ¾ of the lower part of the fruit. Hold dipped apricot over pan, allowing excess chocolate to drip back into the pan.
Transfer the chocolate-dipped apricot to the lined baking sheet. Coat remaining apricots the same way. Allow chocolate to cool, and then chill the apricots until the chocolate is set. Refrigerate until ready to serve.