Project partner Karoon Gas Australia said the Zephyros-1 exploration well in permit WA-398-P was spudded on Monday by the semi-submersible Transocean Legend.
The well lies on the flank of a large tilted fault block about nine kilometres south-west of the Kronos-1 discovery and will test the extent, presence and quality of Plover formation reservoirs.
It follows on from the recent successful drilling of the Boreas-1 well in WA-314-P, which flowed at a constrained stabilised rate of 30.2 million cubic feet per day on a 0.62-inch choke during initial well clean up last month.
Karoon said the Transocean Legend would be used for the entire exploration programme, which was expected to continue through next year.
The next well to be drilled is Proteus-1, which lies in the same block as Zephyros-1, about 14 kilometres south-east of the Poseidon-1 discovery well.
Additional well locations for the remainder of the programme would be announced as joint venture approval was obtained, Karoon said.
ConocoPhillips is the operator of the Poseidon campaign, which entails exploration drilling in permits WA-398-P, WA-314-P and WA-315-P, containing the Poseidon and Kronos gas discoveries.