With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional |ψ|4 theory (which includes quantum Bose gas). In terms of critical density, nc, mass, m, interaction, U, and temperature, T, this shift is universal: Δnc(T) = -Cm3T2U, the constant C found to be equal to 0.0140±0.0005. For quantum Bose gas with the scattering length a this implies ΔTc/Tc = C0an1/3, with C0 = 1.29±0.05.