SafeSpace, formerly known as the Cosby Coalition Against Domestic Violence, started as a grassroots organization serving battered women and their children in a mountainous Appalachian region of East Tennessee.

The group began as an informal network of women helping women in 1976 by providing shelter for victims of domestic violence in their own homes. In 1979 the group organized itself into a task force and in 1981 incorporated as a non-profit, charitable organization. In 1983, SafeSpace accepted an offer of free office space in the City Hall of Newport and the first staff was hired. The shelter was opened on June 25, 1985. The day after the shelter opened, seven women and their ten children were sheltered and it has remained busy since that time. In January of 1986 the board of directors decided to purchase the shelter which was referred to as SafeSpace and eventually the agency changed its original name from the Cosby Coalition Against Domestic Violence to SafeSpace.

SafeSpace was an active and integral part of the movement to end domestic violence from the movement's infancy, especially in the state of Tennessee. SafeSpace was one of the founding members of the Tennessee Coalition Against Domestic and Sexual Violence.