Johnny Damon
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. Nunez retired the Yankee's Johnny Damon, the only batter he faced, on a ground ball to shortstop.