In a saucepan bring broth and water to a simmer and keep at a bare simmer. Cut beet stems into 1/4-inch pieces and slice leaves thin. In a 4-quart heavy kettle cook beet stems and onion in 2 tablespoons oil over moderate heat until stems are tender, about 5 minutes. Add chicken and cook until opaque, about 2 minutes. Add remaining tablespoon oil and beet leaves and saute over moderately high heat, stirring, until leaves are wilted and any liquid is evaporated. Add rice to chicken mixture and cook, stirring constantly, 1 minute. Add wine and cook over moderate heat, stirring constantly, until absorbed. Stir in about 1 cup broth and cook at a bare simmer, stirring constantly, until absorbed. Continue simmering and adding broth, about 1/3 cup at a time, stirring constantly and letting each addition be absorbed before adding next, until rice is tender and creamy looking but still al dente, 18 to 20 minutes. Remove pan from heat and stir in vinegar, grated Parmesan, black pepper, and salt to taste.