In a large saucepan, simmer beats in 3-inches water and half of the vinegar, covered. Cook until beets are tender and can be pierced with a paring knife, about 40 minutes. Uncover and cool beets in the cooking liquid, about 20 minutes. Peel and cut beets into 1/2-inch pieces.
In a bowl, mix the remaining ingredients and toss with the beets. Set aside for 30 minutes to marinate before serving.