A jury will decide how much money, if any, Elizabeth Garcia's family will get from Allsup's Convenience Stores.
She was at an Allsup's Store in Hobbs six years ago, working as a clerk, when she was abducted, raped, and killed.
Her family filed a lawsuit against the New Mexico chain, and seeks money for Garcia's three children.
The family is asking for 60-million dollars, but attorneys representing Allsup's are offering three million.
Elizabeth Garcia disappeared on January 2002.
Her body was found within hours with 57 stab wounds.
Paul Lovett was convicted of her murder, and sentenced to life in prison.