They held the talks before Australia's industrial arbitrator, the Fair Work Commission, and plan further talks on Friday, a union representative said.
This is the second round of talks mediated by the commission in roughly as many weeks. Unions halted weeks of strikes in late September at the facilities that supply around 6% of the world's LNG after an earlier round of talks produced a deal.
However, unions subsequently accused Chevron of reneging on certain commitments and said on Monday they would restart strikes on Oct. 19.
Chevron said on Monday the disagreements only concern a few issues, including reimbursement for travel and meals, and it was committed to reaching a deal.
The strike threat pushed up European gas prices at the start of the week, although they have since fallen in the face of high gas storage and stable Norwegian supply.
