A lot of Native American tribes were matrilineal instead of the typical patrilineal societies you see from Europe. This meant that you were descended from your mother's clan, not your father's. It was also meant the women were involved in the decision-making process for the greater good of the tribe. Some of the more well-known matrilineal socieites are the Lenape, Hopi and Iroquois. The Chickasaw were also a matrilineal society and Chickasaw.TV has a lot of great videos on the subject.
In this first video Jeannie Barbour explains that southeastern tribes share a matrilineal societal organization:
In this video Joshua Hinson talks about how traditionally Chickasaw heritage descended solely from the female:
Jeannie Barbour notes the role of Chickasaw women in battle as communicators and strategists:
The matrilineal structure meant most property belonged to Chickasaw women, not men. When they moved to Indian Territory some Choctaw men wanted to marry these women for their wealth, making the Chickasaw worry about potentially losing their identity.
For more educational videos please visit Chickasaw.TV.