We report results of the magnetic field influence on the chiral spin liquid state in Mn_1–xFe_xSi single crystal with iron content x = 0.108 in proximity of a hidden quantum critical point. The use of small angle neutron scattering data together with magnetic susceptibility measurements down to 0.4 K and precise magnetoresistance measurements in the temperature range 2–20 K in magnetic field up to 5 T allowed us to construct the magnetic phase diagram of this compound in which at low magnetic fields B < 0.15 T an intermediate phase with short-range magnetic order exists in a wide temperature range 0.62 K < T < 9.1 K. It was found that the increase in magnetic field first results in the suppression of a transition to the spiral phase with long-range magnetic order at very low temperatures, and then induces a transition of the intermediate phase to a spin-polarized (ferromagnetic) phase with lowering temperature. The temperature of this transition T_SP increases with magnetic field logarithmically, T_SP ~ log(B), and results in formation of a singular point on the magnetic phase diagram located at T ~ 8.5 K and B ~ 3.5 T, which may be either a triple or a critical point. The possible spin-liquid nature of the intermediate phase is discussed.