The company said it has submitted a petition to have a review performed by Ecuador's National Court of Justice, The Wall Street Journal reported Saturday.
Chevron is also asking that the judgment against it be suspended until an international court, The Hague, can complete its review of the case.
In February 2011, the Permanent Court for Arbitration in The Hague issued a preliminary ordering Ecuador to "take all measures at its disposal to suspend or cause to be suspended the enforcement or recognition within and without Ecuador of any judgment against," the oil company.
Chevron had been previously ordered by a court in Ecuador to pay $9.5 billion for remediation of environmental contamination in the country's Amazon basin rainforest region.
Chevron inherited the responsibility for any damages in the area when it purchased Texaco Inc. in 2001.
Texaco had a presence in Ecuador from 1964 until 1992.
A spokeswoman for the plaintiffs' Karen Hinton said Chevron, "seeks special treatment not afforded any other litigant under Ecuadorean law."
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees
Workers accuse National Zoo of animal mismanagement