To prepare grits, combine 1/2 cup milk, corn, and chipotle chile in a blender; process until the corn is coarsely chopped.
Combine remaining 3 cups milk, 1 1/2 cups water, and 1/2 teaspoon salt in a medium saucepan; bring to a simmer over medium-high heat. Gradually add grits, stirring with a whisk. Cover, reduce heat, and simmer 11 minutes or until thick, stirring frequently. Add corn mixture; cook an additional 3 minutes, stirring frequently. Remove from heat; add cheese and 3 tablespoons sour cream, stirring until cheese melts. Keep warm.
To prepare crawfish, place flour in a large nonstick skillet over medium heat; cook 4 minutes or until lightly browned, stirring frequently. Remove flour from pan; set aside. Wipe pan clean.
Return pan to medium heat. Add oil and sausage to pan; cook 3 minutes, stirring occasionally. Add onion, bell pepper, garlic, thyme, and 1/4 teaspoon salt; cook 3 minutes, stirring occasionally. Add reserved flour, tomato paste, and crawfish; cook 1 minute, stirring frequently. Stir in 1 cup milk; bring to a simmer, and cook 2 minutes or until sauce thickens, stirring frequently. Remove from heat. Stir in 1/4 cup sour cream. Sprinkle 1 tablespoon chives over crawfish mixture. Stir 3 tablespoons chives into grits; serve with crawfish mixture.