Unite said its members at the Ineos site in Grangemouth, Scotland, backed action short of a strike by 90%, with 81% saying they would support stoppages.
The turnout was 86%, said Unite, which has over 900 members at the plant.
The dispute centres on union official Stevie Deans, who was involved in the bitter row with Labour over the selection of a candidate in the Falkirk constituency.
Mr Deans, who is chairman of the constituency party, faces an investigation by Ineos over issues linked to the Falkirk row.
Unite Scottish regional secretary Pat Rafferty said: "This overwhelming result reflects the genuine ill-feeling held by the Grangemouth workforce, because of the grossly unfair treatment of Stephen Deans who has 24 years of loyal service at the site.
"Despite the ongoing threats of plant closures at the Grangemouth site, the workforce are determined to support their colleague and to bring this injustice to an end. This tight knit community has no tolerance for the unfair treatment of a trade unionist because they know that an attack against one is an attack against all.
"The strength of this ballot result should be a wake-up call to management to step back from the brink and stop playing Russian roulette with the Grangemouth site."
Ineos has previously announced it was investigating whether Mr Deans's activities were in line with his role as an employee and union convenor.
The investigation is expected to be completed by October 18 and a decision taken a week later.
The company warned earlier this week that the petrochemical business was at a "crossroads" and faced closure without investment and reductions to its "high cost base."
Ineos said it had invested over £1 billion since taking the site over in 2006 but had lost £150 million each year for the past four years.
The row over the Falkirk constituency selection led to Labour leader Ed Miliband announcing reforms of the party's links with trade unions.
Mr Miliband is proposing that union members will have to opt in to party membership rather than being automatically affiliated, as is currently the case.
The GMB union has already decided to cut its affiliation funds to Labour by over £1 million from next year.
A special conference will be held next March to approve the reforms.
The company said in a statement: "Ineos is disappointed that Unite's Grangemouth members have decided to vote for industrial action over the Stephen Deans investigation.
"The investigation will be concluded by October 25 and is being conducted under a long-established site disciplinary practice and procedure.
"Any industrial action will hurt the site and could lead to closures and job losses."
Calum MacLean, chairman of Ineos Petrochemicals, said: "There cannot be one rule for union officials and one rule for everyone else. We need to be working together to secure the long-term future of the site."