Serve this quick pickle between courses to cleanse the palate.
Wash three pint jars with lids in hot soapy water, and rinse well. (You can use canning jars and lids, but you don't have to.)
Wash fennel, and cut away any bruises or bad spots; trim ends and slice into very thin rings. Cut three 1-inch-long strips of peel from orange. Remove any pith from peel.
Bring 1 1/2 cups water, vinegar, salt, and sugar to a boil in a large pot.
Meanwhile, fill each jar halfway with fennel. Place 1 orange rind and 2 pieces star anise on top of fennel. Fill jar with remaining fennel, using the back of a clean spoon to pack it down. Leave 3/4 inch of space beneath the rim.
Pour hot liquid over fennel, covering it by 1/4 inch and leaving 1/2 inch of beneath the rim of each jar. Place lids on jars, and let stand until cool. Store jars in refrigerator; serve within 3 to 5 days.