Combine the milk, water and salt in a medium saucepan and bring to a simmer over medium-high heat. Whisk in the polenta in a steady stream. Return to a simmer, reduce the heat to low and simmer polenta, partially covered, whisking thoroughly every 3 to 4 minutes. Cook until tender and creamy, about 28 to 30 minutes. Remove from the heat and stir in cheese until melted and smooth. Stir in the chives. Cover and keep warm.
