Slice the fennel into very thin slivers. Thoroughly rinse the fennel and set aside.
Add all remaining ingredients to a small saucepan and bring to a boil. In the meantime, tightly pack the sliced fennel into a glass jar and set aside. Remove the saucepan from the heat and allow the brine to cool slightly, about one to two minutes. Pour the brine into the jar, being sure to cover the fennel completely. Allow to cool to room temperature. Seal the jar with a tight fitting lid. When kept covered and chilled, the pickles will keep well for 1-2 weeks.