Evenly space four 10-inch cinnamon sticks on each of 2 lightly oiled cookie sheets. In a saucepan, combine 1/4 cup water, 2 cups sugar and 1 teaspoon vinegar and stir over moderately low heat until the sugar dissolves; wash down the crystals in the pan with a wet brush. Boil over moderate heat until the syrup is golden and reaches 320°, about 20 minutes. Cool the pan base in cold water for 10 seconds.
Working carefully, use a lightly oiled small ladle to pour 2 tablespoons of the caramel over the tip of each cinnamon stick. Let cool.