Cook pasta in salted boiling water according to packet instructions. Drain, set aside and keep warm.
To make sauce, melt butter in a skillet over low heat, add garlic and cook, stirring, for 1 minute. Stir in cream, lemon juice, Parmesan cheese, chives and lemon rind, bring to a simmer and cook for 2 minutes.
Add parsley and black pepper to taste and cook for 1 minute longer. spoon sauce over pasta and toss to combine.