Cook chorizo in a heavy, medium-size skillet over medium heat until it is crisp, two or three minutes. Transfer chorizo to a paper towel-lined plate to drain. Pour off all but a thin film of fat from the skillet.
Bring a quart of water and a half teaspoon salt to boil in a medium saucepan. Slowly stir in grits. Reduce heat to low and cook about five minutes, whisking occasionally, until grits are thick and smooth. While grits are cooking, add a tablespoon of the butter to skillet and heat over medium-high until butter is foaming.
Cook shrimp in butter until just pink, turning once, about three minutes. Stir in chorizo and garlic and cook, stirring constantly, until garlic is fragrant, about 30 seconds longer. Stir remaining tablespoon butter and cheese into grits and season with salt and pepper. Spoon grits into four warmed bowls and top with chorizo and shrimp mixture. Sprinkle with chives, if desired. Serve immediately.