The Australian Manufacturing Workers Union said thousands of cracks were discovered during routine shutdown and maintenance of Train 2.
The union said the cracks are up to a metre long and 30mm deep and have been found on eight of the kettles, describing it as a "serious failure in a critical piece of kit".
The kettles flow liquid propane, which is highly flammable, through them as part of the process of cooling natural gas to the point where it becomes liquid at -160C.
The union is urging Chevron to close the facility, saying workers on site were fearful for their safety.
In a statement to Energy News the AMWU state secretary Steve McCartney said the kettles that could not be fixed needed to be replaced immediately.
"Chevron needs to put workers' safety first and shut down for an independent investigation. If something goes wrong it could be catastrophic."
Chevron Corporation told Energy News the relevant regulatory bodies have been informed of the cracks and inspections were ongoing.
The planned shutdown of Train 2 started in May, with a company spokeswoman saying Chevron was "pleased with the strong progress made to date".
She said the company has scheduled a maintenance turnaround every year for the next four years.
Production from Gorgon LNG Trains 1 and 3 have been unaffected, however the AMWU said the kettles currently in use on the trains are the same design and built at the same factory in South Korea as the cracked ones on Train 2.
"If multiple kettles are showing cracks in testing on Train 2, there is a high risk there are cracks in the vessels on other trains," McCartney said.
Shipyards and factories in South Korea have been responsible for much of the kit in Australia's LNG plants, and the Samsung Heavy Industries yard in Geoje built Shell's flagship floating LNG vessel the Prelude.
A report released last year by the International Petroleum Industry Environmental Conservation Association (IPIECA) found engineering, procurement and construction phases of a project carried the highest level of risk faced by workers, due to large labour input from low-skilled workers hired by contractors and subcontractors.
Chevron and other majors are all members of IPIECA, which aims to promote high environmental and social standards within industry.
The Chevron spokeswoman said learning from the current maintenance event will inform future turnarounds and afford the same opportunities for improvements.
At the beginning of the year, workers on board a Gorgon drilling rig operated by subcontractor Transocean were forced to wear protective breathing apparatus to prevent "an immediate threat to health and safety" according to the offshore regulator.
The National Offshore Petroleum Safety and Environmental Management Authority (NOPSEMA), which issued the notices, said a planned inspection of the Development Driller 1 rig found "airborne hazardous chemical dust" which was not being controlled during a chemical mixing operation.
Transocean and Chevron immediately implemented what is known as a ‘work around' requiring workers conducting chemical mixing to wear respirators.