NEW YORK (Reuters) - A federal judge on Thursday said Chesapeake Energy Corp (>> Chesapeake Energy Corporation) must pay an additional $59.1 million to some investors whose bonds it redeemed early, boosting the natural gas company's total payout to $438.7 million.

U.S. District Judge Paul Engelmayer in Manhattan said the new payment reflects prejudgment interest at a 6.775 percent annual rate.

Engelmayer had ruled on July 10 that Chesapeake should pay nearly $379.7 million plus the interest to holders of its $1.3 billion of 6.775 percent notes maturing in 2019.

The judge ruled after a federal appeals court last November said Chesapeake had waited one month too long to tell investors it planned to redeem the notes six years early.

Bank of New York Mellon Corp (>> Bank of New York Mellon Corp) was the trustee for the bondholders. It had argued that Oklahoma City-based Chesapeake should pay a special, higher price because of the redemption.

Chesapeake intended to redeem the bonds early to reduce a debt burden accumulated under former Chief Executive Aubrey McClendon, and offset falling natural gas prices.

The case is Chesapeake Energy Corp v. Bank of New York Mellon Trust Co, U.S. District Court, Southern District of New York, No. 13-01582.

(Reporting by Jonathan Stempel in New York; Editing by Bernard Orr)