Computer simulation results are presented for the phase behavior of a symmetric binary mixture of nonadditive hard spheres. In this model, the hard sphere diameters are given by sigma(AA)=sigma(BB)=lambdad and sigma(AB)=d. At high densities and for small enough lambda, this hard sphere mixture exhibits a fluid-fluid phase separation into an A-rich and a B-rich phase. Semigrand ensemble simulations are performed for the critical point and the phase behavior of this model for various values of lambda. The results for the critical density are significantly different from previous simulation estimates. A comparison of our simulation results to existing theories shows that none of the theories are accurate for the location of the critical point, over the entire range of lambda. (C) 2003 American Institute of Physics.