According to the Australian, the energy giant has employed the semi-automated Ensign Rig 48 for the campaign, which comprises eight water injector wells and five production wells.
The first well was spudded in September and Chevron expects to complete drilling next month, the newspaper reported.
Future infill programs are reportedly scheduled for 2010 and 2012.
Discovered in 1964, the Barrow Island oil field was originally forecast to have a 30-year life, but is now expected to last until the 2020s thanks to good reservoir management.
