The company wants the justices to reverse a lower court ruling that Jamie Leigh Jones' case can go to trial. Jones sued Halliburton and its former subsidiary KBR, saying she was raped while working for KBR at Camp Hope, Baghdad, in 2005.
The trial is set to begin in February 2011.
Halliburton says the contract signed by Jones and other workers requires claims to be settled through arbitration, not trial.
The 5th U.S. Circuit Court of Appeals in New Orleans ruled in Jones' favor in September.
The Associated Press usually doesn't identify people alleging sexual assault, but Jones' face and name have been broadcast in media reports and on her own Web site.
The case is KBR Technical Services v. Jones, 09-864.
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