We report the experimental observation of temporal vector soliton propagation and collision in a linearly birefringent optical fiber. To the best of the authors' knowledge, this is both the first demonstration of temporal vector solitons with two mutually incoherent component fields, and of vector soliton collisions in a Kerr nonlinear medium. Collisions are characterized by an intensity redistribution between the two components, and the experimental results agree with numerical predictions of the coupled nonlinear Schrödinger equation.