The Oklahoma City-based arts-and-crafts chain asked a federal appeals court Thursday for an exemption from part of Obamacare.
Hobby Lobby leaders believe they should not be required to offer employees health insurance that covers abortion-inducing drugs, or certain kinds of intrauterine devices.
The company argues that businesses, and not just religious groups, should be allowed to be exempt from that part of the healthcare law when it violates their religious beliefs.
But lower courts have rejected Hobby Lobby's claim, saying the exemption is for religious organizations like churches, but does not include for-profit businesses which primarily employ members of the faith.
Last year a federal judge concluded a decision by saying, "Hobby Lobby and Mardel are not religious organizations."
Kyle Duncan, who argued before the U.S. 10th Circuit Court of Appeals on behalf of the owners, said, "They ought to be able - just like a church, just like a charity - to have the right to opt out of a provision that infringes on their religious beliefs."
Hobby Lobby is a "biblically founded business" opening in 1972. They operate more than 500 stores in 41 states and employ more than 13,000 full-time employees eligible for health insurance.
All stores close on Sundays.