The absence of centrosymmetry in the enantiopure chiral magnet [N(CH3)(n-C3H7)(2)((CH)-H-star(CH3)C2H5)][(MnCrIII)-Cr-II(ox)(3)] allows the observation of bulk second harmonic generation (SHG) in this material. At low temperature, the onset of magnetization gives birth to a magnetization-induced SHG (MSHG) contribution. With an angular shift of 13.1 degrees upon magnetization reversal, the MSHG effects appear to be much larger than the corresponding linear magneto-optical effects. Thanks to the single-crystalline state of the sample, the variation of the signal with the orientation of the magnetic field and/or the angle between the polarization of the incident radiation and the outgoing SHG signal in the paramagnetic and ferromagnetic phases is reproduced and well-understood through the use of a symmetry-based analysis of the nonlinear susceptibility tensor.