The jungle residents, including the Cofan Indian tribe, accuse Chevron's Texaco subsidiary of dumping 18 billion gallons of oil-laden water into their Amazonian region between 1972 and 1992.
The nearly 30,000 jungle dwellers demand damages to help with clean-up costs.
Oil firm rejects accusations
Texaco merged with Chevron in 2001 and the company denies any wrongdoing.
Rafael Correa, a political outsider, promised to visit the Amazon region later this month [AFP]
"Texaco complied with its obligations and successfully remediated its share of the oil operations in the Oriente," Kent Robertson, a Chevron spokesman, said.
"After the remediation was shown to be successful, the government of Ecuador released Texaco of any environmental liabilities.
"We believe the government of Ecuador should comply with its contractual obligations."
The long-running lawsuit is being litigated at a local court and plaintiffs' lawyers said a ruling could come as early as the second half of this year.
Correa, a US-educated economist, has worried foreign oil companies with pledges to rework contracts in an effort to boost the government's share of oil revenues.
Chevron no longer operates in Ecuador, South America's fifth-largest oil producer with an output of around 530,000 barrels of oil per day.