Chop the chocolate into small pieces and melt it over a pan of hot water (or heat up in a microwave, checking on the consistency at regular intervals. Once chocolate has melted, remove from hot water and allow it to cool slightly.
Separately, peel the oranges and break them up by the segments. Clean the segments of any white orange peel threads. Place in a clean plate.
While waiting for the chocolate to cool slightly, prepare parchment paper and baking rack. Cut parchment paper into small squares (enough to fit one orange segment each) and place the cooling rack over a large plate. The plate is to catch excess chocolate that drips of the orange segments placed on the wire racked after dipping into chocolate.
Once the chocolate as cooled slightly, hold the orange segments at one end and dip into chocolate, just enough to cover the orange segment to desired height. Lift the orange segment out of the chocolate, hold for a few seconds for excess chocolate to drip off and carefully place the dipped orange segment on a cooling rack to allow excess chocolate to continue to drip off. Repeat the process until all the orange segments have been dipped in chocolate.
Next, lift the chocolate covered orange segments and place them on the parchment paper prepared earlier. Arrange on a wide plate and place them in the refrigerator for about 10 minutes, until the chocolate sets.
Remove from fridge and peel off the parchment paper. Arrange the chocolate dipped mandarin oranges in a serving plate to serve.