Chevron holds roughly 700,000 net acres in the Delaware Basin in New Mexico and added 246,000 acres in the deal with Chesapeake.
Chevron said the New Mexico acreage is producing 7,000 barrels of oil equivalent per day. The company said the potential exists to increase that volume "substantially" over the next few years.
"This acquisition in a premier emerging play in the Permian Basin grows our significant leasehold position there," Chevron Vice Chairman George Kirkland said in a statement.
In a separate deal, Chesapeake sold 618,000 net acres in the Permian Basin in western Texas to Royal Dutch Shell for $1.93 billion. Shell said the region in Texas is producing around 26,000 barrels of oil equivalent per day with significant growth potential.
Chesapeake said it was closing a series of deals to sell some assets. It said in a statement that is sold holdings in the Utica shale deposit in a deal with French supermajor Total for about $200 per acre.
Chesapeake Chief Executive Officer Aubrey McClendon said the net proceeds from sales in 2012 total around $11.6 billion.
"These transactions are significant steps in the transformation of our company's asset base to a more balanced portfolio," he said in a statement.