Jones says she was raped while working for KBR at Camp Hope, Baghdad, in 2005. KBR and Halliburton, both based in Houston, split in 2007.
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 website.
The companies deny Jones' allegations and contend her contract required claims against them to be settled through arbitration.
The lawsuit, filed in 2007, has been delayed by various appeals.