The US independent said the production unit turned on the taps on 14 January.
"Heidelberg achieved first oil significantly ahead of schedule and favorable to budget," Anadarko said in a brief statement.
The facility, sister to the Lucius spar that started up last year, is situated in Green Canyon Block 859 in 5300 feet of water.
It has capacity for 80,000 barrels of oil and 80 million cubic feet per day of natural gas.
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