Penny signed a three-year contract for Burnley on 27 June 2008, making his debut on 9 August 2008 in a 4–1 loss against Sheffield Wednesday. After his debut, throughout the 2008–09 season and into his second year with Burnley, he was second-choice to Brian Jensen. Penny made his Premier League debut in the 2009–10 season, after coming on for the injured Jensen in a 3–1 home defeat to Wigan Athletic. On 16 August 2010 he left Burnley by mutual consent and returned to his homeland of Peru. Penny made a total of 4 appearances for Burnley in all competitions.