Preheat gas grill on high heat. Turn one burner off, then reduce the other burner(s) to medium.
Individually wrap each beet in foil. Place beets over the off area and cover. Cook, turning the beets occasionally, until just tender, 45-60 minutes. Cool completely. Peel and slice beets into 1/2 inch thick rounds.
In a medium bowl, whisk balsamic vinegar, tarragon, brown sugar, salt and pepper until combined. Gradually whisk in oil until dressing thickens. Add beets and onions and toss well.
Cover and refrigerate until chilled, at least one hour. Serve chilled.