Buttermilk adds a subtle, creamy tang to the grits.
Bring water, whole milk, and salt to a boil in a medium saucepan over medium-high. Gradually whisk in uncooked grits; return to a boil. Reduce heat to medium-low, and simmer, stirring occasionally, until creamy and thickened, 25 to 30 minutes; stir corn into grits during last 5 minutes of cooking. Remove from heat, and stir in buttermilk and butter.
Stir chèvre and chives into warm grits just before serving.