The announcement comes after its board unanimously determined that Occidental Petroleum's rival bid, launched last week, could reasonably lead to a proposal that is superior to Chevron's previously announced deal to buy Anadarko.
Occidental has offered $76 a share for Anadarko, while Chevron has put $65 a share on the table.
The board's determination allows Anadarko and its advisers to resume talks with Occidental under the terms of the Chevron deal. The agreement with Chevron remains in effect, and Anadarko's board reaffirmed its support for the deal for the time being. Anadarko would have to pay Chevron a $1 billion breakup fee if it decides to sell to Occidental.
The announcement is the latest development in a rare bidding war in the oil and gas sector. At the heart of the battle are the crown jewels of Anadarko's portfolio: a significant footprint in the Permian Basin, the top U.S. shale oil field.
Both Chevron and Occidental are seeking to expand their presence in the Permian, which stretches across western Texas and southeastern New Mexico. Occidental CEO Vicki Hollub told CNBC that Anadarko's Permian assets represent about 75 percent of the deal value.
Analysts say Chevron may have to sweeten its offer for Anadarko. During a conference call on Friday, company executives declined to offer details on the price they'd be willing to pay. However, Chevron CEO Michael Wirth said the oil giant would bow out if the cost of buying Anadarko got too high and no longer created value for shareholders.
Occidental revealed last week that it had put forward three offers to buy Anadarko since late March. On Monday, Anadarko said the latest proposal "reflects significant improvement" in value, terms and conditions, and closing certainty compared to previous offers.
Anadarko stressed that its decision to restart negotiations with Occidental does not assure the talks will produce a deal that is superior to the agreement with Chevron.
Hollub says Occidental is the best acquirer for Anadarko because her company is a top performer in the Permian and can squeeze the best results out of the company's wells. Chevron believes it can bring industrial scale to that shale acreage and says Anadarko's other assets — including in the Gulf of Mexico and Mozambique — better align with its portfolio.
"We believe our signed agreement with Anadarko provides the best value and the most certainty to Anadarko's shareholders," Chevron said in a statement on Monday.
Shares of Chevron and Anadarko were up slightly Monday while Occidental's fell 2%.