The giant U.S. oil company objected last June when Washington proposed allowing duty-free rose imports from the world’s poorest countries, including Ecuador. A decade earlier, an Ecuadorean court had blamed Chevron for oil pollution and told it to pay $9.5 billion in damages, one of the largest-ever penalties of its kind. Chevron had since proved the verdict fraudulent, it told the U.S. Trade Representative. But Ecuador refused to render it unenforceable despite an order to do that from an international arbitration tribunal. Letting Ecuador save money on flowers after blatant “acts of defiance” would tell the world the U.S. rewards bad behavior, the oil company said. Chevron lost the war of the roses. But it still hasn’t paid a cent of the Ecuadorean judgment, and says it won’t stop legally battling until it can ensure that it never has to.

“We’re going to fight this until hell freezes over, and then we’ll fight it on the ice,” a former Chevron general counsel, Charles James, said before his retirement in 2010, a remark that became a watchword at the company. His successor, R. Hewitt Pate, said this spring that “only the government of Ecuador could deliver a final resolution of this case,” by nullifying the verdict.

Big companies that see lawsuits against them as unfounded often reach a point, after losing a court ruling or two, when settling seems the sensible course. Chevron never did. Twenty-eight years after the Ecuador case was filed, 10 years after it came to a verdict and seven years after Chevron got a different court to find egregious misbehavior by a plaintiffs’ lawyer, Chevron fights on—pressing to make sure that lawyer doesn’t profit from the case, hiring attorneys in countries where it operates and where plaintiffs might try to collect, trying to force Ecuador to pay its legal costs and, as with the roses, asking the U.S. government to penalize Ecuador in the trade arena.

Chevron’s opponents also refuse to back down, making the case what appears to be the oil industry’s longest-running legal slugfest. Aspects of it have been heard by some 100 judges in 36 courts in seven countries. By Chevron’s estimate, it has cost the company nearly $1 billion, including 1.5 million hours of its staff, advisers’ and attorneys’ time. Executives and lawyers who worked on the case have retired or died since it began. Although the oil industry’s era of global power seems to have peaked, for Chevron part of that era—costly, intractable environmental-pollution litigation—continues unabated. The Ecuador legal fight has lasted even longer than the one that followed the Exxon Valdez oil spill in Alaska.

Well before Chevron lost the damage verdict in 2011, it set out to turn the tables on the litigants. It subpoenaed or sued dozens of people who had helped the plaintiffs’ side, legal records show, and unearthed damaging video clips about the plaintiffs’ legal team’s activities from documentary-film outtakes. Chevron’s lawyers obtained the personal notes of the lead plaintiffs’ lawyer, Steven Donziger, and used his own words against him.

The company scored a seminal victory in 2014 when a federal judge in New York found that Mr. Donziger and others on his team had offered a bribe to a judge in Ecuador and had ghost-written the court verdict.

Mr. Donziger’s New York law license was revoked. He faces a criminal contempt-of-court trial this month over his refusal to turn over records to Chevron as ordered. His bank accounts were frozen. He has been under house arrest for nearly two years, unable to leave his Manhattan apartment without court permission, an ankle bracelet tracking his every move.