We calculate the nonlinear galaxy power spectrum in real space, including nonlinear distortion of the baryon acoustic oscillations, using the standard third-order perturbation theory (PT). The calculation is based upon the assumption that the number density of galaxies is a local function of the underlying, nonlinear density field. The galaxy bias is allowed to be both nonlinear and stochastic. We show that the PT calculation agrees with the galaxy power spectrum estimated from the Millennium Simulation, in the weakly nonlinear regime (defined by the matter power spectrum) at high redshifts, 1 ≤ z ≤ 6. We also show that, once three free parameters characterizing galaxy bias are marginalized over, the PT power spectrum fit to the Millennium Simulation data yields unbiased estimates of the distance scale, D, to within the statistical error. This distance scale corresponds to the angular diameter distance, D_A (z), and the expansion rate, H(z), in real galaxy surveys. Our results presented in this paper are still restricted to real space. The future work should include the effects of nonlinear redshift space distortion. Nevertheless, our results indicate that nonlinear galaxy bias in the weakly nonlinear regime at high redshifts is reasonably under control.