Transfer the chicken and the onions with a slotted spoon to a heated platter and keep them warm, covered with foil. Stir the arrowroot or cornstarch mixture, add it to the simmering cooking liquid with half the chopped fresh tarragon, if using, and simmer the sauce, stirring, for 1 minute. Spoon the sauce over the chicken, sprinkle the chicken with the remaining chopped fresh tarragon, if using, and garnish it with the tarragon sprigs.