Chevron spokesman James Craig told AFP the request to Judge Nicolas Zambrano will suspend enforcement to allow the company time to appeal the decision.
"Once the judge responds, we will have 72 additional hours to appeal," he said. In the meantime, he added the judgment is suspended.
The court on Monday announced a landmark penalty against Chevron of $8.6 billion with an addition 10 per cent for environment management costs in the suit that dates back to 1993 against Texaco, a firm acquired by Chevron.
Plaintiffs in the case, which include indigenous communities in Ecuador, also plan to appeal, saying the ruling fails to adequately compensate for certain damages and illness.
They were seeking more than $27 billion for pollution damage caused by Texaco's oil extraction between 1964 and 1990.
Chevron claims it was absolved of liability because Texaco paid $40 million in cleanup efforts, approved by the government, before it was bought by Chevron.
The US firm has said the judgment "is illegitimate and unenforceable" and is "contrary to the legitimate scientific evidence."