The company took the name of the animal preservation and land plantation owned by philanthropist and Baryshnikov friend Howard Gillman. Gilman built a beautiful dance studio on his White Oak Plantation near Jacksonville, Florida for the company to create its first tour. White Oak became a premier location to workshop works being created by many of the world's leading choreographers.
The company continued to tour until 2002, allowing the Foundation to concentrate on the 2004 opening of the Baryshnikov Arts Center in Manhattan. The company featured alumni of major dance companies and commissioned new pieces from Morris, Paul Taylor, Twyla Tharp, Jerome Robbins, David Gordon and others.