Workers on Thursday voted to authorize the Offshore Alliance of unions to call a strike at Chevron's Gorgon and Wheatstone projects.
In a Facebook post, the union alliance said of Chevron's senior management team: "Their stupidity is about to cost them $billions in lost production and profit."
The unions also criticised the company for putting a proposal directly to a worker vote without going through the bargaining process, and the unions threatened industrial action.
Chevron did not immediately respond to a request seeking comments outside normal business hours.
More than 99% of some 450 workers voted in favour of a authorizing a strike, which could include refusing to load tankers or vessels, bans on certain tasks and a full strike.
The Offshore Alliance, which combines the Maritime Union of Australia and Australian Workers' Union, must give Chevron seven working days' notice before a strike.
The escalation comes a day after the Offshore Alliance reached an in-principle agreement at Woodside's (WDS.AX) North West Shelf LNG facility, Australia's largest, triggering a sharp fall in Dutch and British wholesale gas prices on Thursday.
Any strike would have forced Asian buyers to outbid Europe to attract cargoes. China and Japan are the top two lifters of Australian LNG, followed by South Korea and Taiwan.
North West Shelf along with Chevron's Gorgon and Wheatstone projects account for about one-tenth of global supplies.
Energy analyst Saul Kavonic said Chevron could face some "low-level" industrial action but that was unlikely to significantly disrupt supplies.
"The public rhetoric will once again ramp up as the Chevron negotiations get underway, as a normal part of the Australian union bargaining process," he said.
