Put the turnips, chicken stock, 1/2 tablespoon of the butter, sugar and 1/2 teaspoon salt in a medium skillet. Bring to a boil over medium-high heat. Reduce the heat to a bare simmer and cook, covered, until the turnips are just tender, about 10 minutes. With a slotted spoon, transfer the turnips to a bowl.
Increase the heat to medium high and boil the remaining chicken stock until it reduces to 2 tablespoons, about 7 minutes. Off the heat, return the turnips to the skillet. Add the remaining tablespoon butter and the tarragon; stir until the butter is melted and the turnips are well coated. Garnish with additional chopped tarragon.