The decision leaves Occidental as a victor in a race that once again demonstrated the attractiveness of the American shale.
The decision also means Chevron will collect a $1 billion breakup fee, a windfall that it could use to purchase another driller in the Permian Basin, the engine of the American oil drilling boom.
Chevron will not increase its offer for Anadarko from CNBC.
Occidental Petroleum Corporation (Occidental) is an oil and gas exploration and production company. The Company operates through three segments: oil and gas, chemical (OxyChem), and midstream and marketing. The oil and gas segment explores for, develops and produces oil and condensate, natural gas liquids (NGLs) and natural gas.