Combine 4 cups water and salt in a large saucepan over medium-high heat; bring to a boil. Gradually add polenta, stirring constantly with a whisk. Reduce heat, and cook 8 minutes or until thick, stirring frequently. Remove from heat. Add 1 tablespoon butter; stir until butter melts. Keep warm.
Melt remaining 2 tablespoons butter in a large skillet over medium heat; cook 3 minutes or until lightly browned, stirring occasionally. Add chopped shallots to pan, and cook 2 minutes or until browned, stirring frequently. Add cremini mushrooms to pan; cook 4 minutes or until lightly browned, stirring frequently. Combine chicken broth, juice, and cornstarch in a small bowl, stirring until smooth. Stir broth mixture into mushroom mixture, and bring to a boil. Cook for 1 minute, stirring constantly. Remove from heat, and stir in 2 tablespoons chives.
Place about 1/3 cup polenta in each of 8 bowls; top each serving with about 1/4 cup mushroom mixture. Sprinkle each serving with chopped fresh chives, if desired.