We have developed a method for measuring the spin wave stiffness in helimagnets with Dzyaloshinsky-Moriya interaction in a completely polarized state using small-angle scattering of polarized neutrons [1]. It has been experimentally proved that the dispersion of magnons in this state has an anisotropic appearance, since the neutron scattering intensity pattern is registered as two circles for neutrons with the gain and loss of the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer value equal to the helix wave vector ± ks, which is oriented along the applied magnetic field H. The radius of the circles is directly related to the spin wave stiffness of the magnetic system, but depends on the magnitude of the magnetic field. This scattering depends on the polarization of neutrons, showing the chiral nature of the spin waves in the Dzyaloshinsky-Moriya helimagnet in the polarized state.