Gather all ingredients.
Sprinkle chicken with ½ tsp. salt and pepper. Melt 1 tablespoon butter in a large skillet over medium-high heat. Add chicken; cook 6-8 minutes, until chicken is browned and cooked through. Remove chicken from pan and set aside. Do not wipe pan clean.
Meanwhile, cook pasta according to package instructions for al dente, adding 2 teaspoons kosher salt to water. Before draining the pasta, measure out ½ cup pasta water and set aside.
Melt remaining ¼ cup butter over medium-high heat. Add shallot, smoked paprika, crushed red pepper, and remaining ¼ teaspoon salt; cook 5 minutes until softened. Add garlic and cook 1 minute longer. Stir in lemon juice and zest; cook 1 minute, stirring constantly.
Add cream and bring to a light simmer over medium heat, stirring frequently until thickened slightly, about 5 minutes. Gradually stir in cheese until melted and smooth. Stir in chicken, 1 tablespoon chopped parsley and chives.
Add drained pasta to chicken mixture. Turn heat to low, stir in ¼ cup pasta water, and toss until pasta is coated in sauce, cooking 2-3 minutes longer. If sauce is too thick, add additional pasta water, 1 tablespoon at a time, until desired consistency has been reached. Serve sprinkled with remaining 1 tablespoon parsley.