Data from the Warrior-1 well in WA-390-P, which was drilled by the semi-submersible rig Jack Bates, showed the presence of gas though not in significant quantities.
Hess will now take the findings of all four wells it drilled and integrate the data with the 3500 square kilometre 3D seismic it shot earlier this year to help shape its program for 2009.
A Hess spokesman told PetroleumNews.net that it was still "early days" for the company in the permit and added that it could resume operations sometime in the second quarter of 2009.
The company's first three wells all struck gas though the company did not carry out any flow testing. The Glencoe-1, Briseis-1 and Nimblefoot-1 wells intersected 28m, 46m and 28m of net pay respectively.
Hess holds a 100% interest in the 780,000-acre permit, which is next to the giant Jansz/Io discovery held by the Gorgon partners, Chevron Australia, Shell Development Australia and ExxonMobil, and due west of the Greater Gorgon gas field.
It secured the permit last year with a giant 16-well drilling commitment that set new Australian work and financial obligation records.