The Green Canyon Block 807 Well No. 2 encountered oil pay in multiple Lower Tertiary Wilcox Sands.
The well is located approximately 225km off the coast of Louisiana in 1,580m of water.
Well No.2 was drilled to a depth of 10,287m. Appraisal drilling is due to start later this year.
Chevron USA operates the Anchor prospect with a 55% working interest, while Cobalt International Energy owns a 20% stake.
Samson Offshore Anchor and Venari Resources each have a 12.5% interest in the prospect.
Chevron upstream senior vice-president Jay Johnson said: "The Anchor discovery, along with the previously announced Guadalupe discovery, are significant finds for us in the deepwater Gulf of Mexico.
"We had one of our best years with the drill bit in 2014, reporting more than 30 discoveries worldwide and adding an estimated one billion barrels of new resources to our holdings."
Chevron presently has five deepwater drillships operating in the Gulf, two of which are focused on exploration activities.
In October 2014, Chevron and its partners unveiled that they will invest an estimated $6bn in the development of the Stampede project, also in the deepwater US Gulf of Mexico.
The Stampede field has estimated recoverable resources of more than 300 million barrels of oil equivalent.