 On July 31, 2008, Núñez was traded to the New York Yankees for infielder Alberto Gonzalez and joined the Yankees Double-A affiliate, the Trenton Thunder.On November 13, 2008, Núñez was traded along with Wilson Betemit and Jeffrey Marquez to the Chicago White Sox for Nick Swisher and Kanekoa Texeira.He made his major league debut for the White Sox on August 2, 2009, at U.S. Cellular Field.