A group of women is suing the world's biggest retailer, Walmart, claiming they were held back because of their gender.
They want to bring a class action suit on behalf of more than a million women.
Walmart denies the allegations, saying it has a long history of promoting women and paying them well.
Christine Kwapnowski, one of six women named as plaintiffs in the lawsuit, claims she was passed over for pay and promotion in favour of male colleagues.
"I asked what I needed to do to get promoted and my manager said I should 'doll up and blow the cobwebs off my make-up'," she told the BBC.
The group bringing the lawsuit believes Walmart systematically discriminated against women in stores across America.
The six are making their claim under the 1964 Civil Rights Act, arguing "the policies and practices underlying this discriminatory treatment are consistent throughout Walmart".
The women, who are seeking lost pay and damages, want the US Supreme Court to allow the case to proceed a class action lawsuit against Walmart.
A class action would cover any woman who has worked for, or works for, the store.
The claims of discrimination are vehemently denied by Walmart, which points out that it has won awards for its women-friendly working practices.
"Walmart has had - for many years - strong policies against discrimination and these policies are there to ensure women are promoted and paid well," company spokesman Greg Rossiter said.
Walmart argues that a class action lawsuit would unnecessarily include women who do not have a grievance against the firm.