Line a baking sheet with waxed paper; set aside. In a small microwave-safe bowl microwave chocolate on 50 percent power (medium) for 1 1/2 to 2 minutes or until melted and smooth, stirring every 30 seconds.
Dip each apricot half halfway into melted chocolate; place on prepared baking sheet. Sprinkle evenly with ground chile pepper. Let stand about 1 hour or until set.