We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to seventh order and find the point where an isotherm satisfies the critical conditions. Second, we use Gibbs ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K for real helium), the critical pressure is 0.93 MPa, and the critical density is 28.4 mol.L-1, with expanded uncertainties (corresponding to a 95% confidence interval) on the order of 0.1 K, 0.02 MPa, and 0.5 mol.L-1, respectively. The effect of three-body interactions on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at higher temperatures where quantum effects are expected to be negligible. In these situations, the distortion of the critical properties by quantum effects causes problems for the correspondingstates treatment.