Anadarko (APC) announced on Monday it plans to enter merger talks with Occidental Petroleum(OXY), which made a hostile takeover offer for the oil driller last week.

This means Anadarko Petroleum could walk away from its marriage with Chevron.

The Occidental cash-and-stock bid values Anadarko at nearly $57 billion. That's about 20% more than the takeover deal Anadarko already reached with oil giant Chevron (CVX) earlier this month.

The bidding war for Anadarko reflects an intense desire by oil companies large and small to acquire America's best shale assets. Specifically, oil companies are racing to drill oil in the Permian Basin, the West Texas shale oilfield that has made the United States the world's leading producer.

Anadarko and Occidental had been in merger talks even before Chevron reached a takeover deal for Anadarko.

Now, Anadarko said it will resume negotiations with Occidental, which is already the No. 1 oil producer in the Permian Basin. Acquiring Anadarko's Permian assets would lift Occidental's output in that shale oilfield to 533,000 barrels per day.

Even though neither Anadarko nor Occidental are household names, a merger would create an oil behemoth. The combined company would be worth about $100 billion and produce about 1.4 million barrels of oil per day.

After reviewing the Occidental bid with lawyers and bankers, Anadarko's board of directors said it has unanimously determined it could reasonably be expected to result in a "superior proposal."

In a statement, Anadarko's board said the Occidental bid reflects "significant improvement" in terms of value, terms, conditions and closing certainty over Occidental's previous proposals.

Last week, Occidental offered to purchase each Anadarko share for $38 in cash and 0.6094 of a share of Occidental's stock.

Chevron's deal is more skewed toward stock. Chevron offered to pay $16.25 in cash and 0.3869 of a share of its stock for each Anadarko share.

In a statement, Chevron expressed confidence its deal will prevail.

"We believe our signed agreement with Anadarko provides the best value and the most certainty to Anadarko's shareholders," Chevron said on Monday.

Anadarko cautioned that there "can be no assurance" that talks with Occidental will result in a better deal than the one already reached with Chevron.

Despite the new negotiations with Occidental, Anadarko said the Chevron merger agreement remains in effect. The Anadarko board reaffirmed its recommendation in favor of the Chevron deal "at this time."

Wall Street analysts have expressed concern that Occidental's deal could strain the company's balance sheet. Acknowledging that challenge, Occidental CEO Vicki Hollub told analysts last week that the company would "rapidly deleverage" by selling off between $10 billion and $15 billion of assets over two years.

As America's No. 2 oil company, Chevron certainly has the firepower to sweeten its bid. But Chevron must also guard against overpaying for Anadarko and its energy portfolio.

Beyond its Permian Basin position, Anadarko is attractive because of its shale assets in Colorado, deepwater drilling properties in the Gulf of Mexico and liquefied natural gas project in Mozambique.

Last week, Chevron executives suggested Anadarko would be a better fit with their company. Chevron pointed to its track record for making successful acquisitions and role as a top-notch LNG producer.

If Anadarko goes with Occidental, Chevron won't be left empty-handed. Under the terms of their merger agreement, Anadarko would owe Chevron a break-up fee of $1 billion if it reaches a takeover deal with another company.

Shares of Occidental fell about 2% on Monday, while Chevron and Anadarko were little changed.