The short answer is that Native Americans owned slaves. The situation, however, is complicated, as there were many different Native American groups on the North American continent with different attitudes towards slavery, Native Americans were themselves enslaved, and the nature of Native American slavery changed after contact with Europeans.
Before Europeans took over, Native American slavery was more akin to slavery in the ancient Middle East. Slaves were acquired through conquest or to settle debts. They were war booty as opposed to racially inferior and often were gradually assimilated into the tribe.
After the Europeans took over, Native Americans themselves were purchased or captured as slaves. A famous eighteenth-century story describing Native American enslavement, called "Inkle and Yarico," was picked up by abolitionists: in it, Inkle, an Englishman, is helped by a Native American woman named Yarico, who he impregnates, only to turn around and sell her and his unborn child in the slave market. Native Americans, however, made unreliable slaves because they knew how to escape captivity.
Native Americans were also known to enslave captured whites, a prospect which frightened eighteenth-century Quaker John Woolman, who was embarking on a religious visit to Native tribes during a period of unrest. (Although very nervous, as he describes in his Journal, he nevertheless followed the prompting of the Holy Spirit and visited the natives, had a good visit, and avoided being enslaved.)
Among tribes that were more prone to want to assimilate to European ways, such as the Five Tribes (sometimes called the Five "Civilized" Tribes: Chickasaw, Cherokee, Choctaw, Creek, and Seminole) use of black slaves on the European model was adopted. Black slaves were owned by tribe members and used as domestic workers and to harvest crops.