Peacock attended Palm Beach Central High School, where he played third base. Peacock requested that his coach try him at pitcher, and he threw eight innings in high school prior to pitching in a summer league.

Peacock was drafted by the Washington Nationals in the 41st round of the 2006 Major League Baseball Draft.

Peacock did not play in the Nationals' system in 2006. He spent the 2007 season with the GCL Nationals, Washington's affiliate in the rookie-level Gulf Coast League, accruing a record of 1 win and 1 loss and a 3.89 ERA. Over 39⅓ innings in 2007, consisting of seven starts and six appearances in relief, Peacock struck out a total of 34 batters and issued just 15 bases on balls.

Baseball America rated Peacock the 42nd best prospect in baseball during the 2011 season. He represented the Nationals at the 2011 All-Star Futures Game. He was named a starting pitcher on Baseball America's 2011 Minor League All Star team.

Peacock was promoted to the majors and made his MLB debut on September 6, 2011.

On December 23, 2011, Peacock was traded with Tommy Milone, Derek Norris, and A. J. Cole to the Oakland Athletics for Gio Gonzalez and Robert Gilliam. He did not play at all in the major leagues for the Athletics in 2012.

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