The independent giant started drilling the Poseidon North-1 well off the coast of Western Australia on Wednesday.
The well is targeting the Plover and Montara formations in permit WA-315-P, on the crest of a large, tilted fault block.
Poseidon North-1 is just north-east of the Poseidon-1 well.
The six-well programme will continue through the year. Four of six wells have been completed so far.
ConocoPhillips