A graduate of Harvard Law School and an elected member of the American Law Institute, Nielson was an appellate partner at Kirkland & Ellis LLP and a law clerk to Justice Samuel A. Alito, Jr. of the U.S. Supreme Court, Judge Janice Rogers Brown of the U.S. Court of Appeals for the D.C. Circuit, and Judge Jerry E. Smith of the U.S. Court of Appeals for the Fifth Circuit.