We report strong diffraction of cold neutrons from an only 30 micrometer thick holographic polymer-dispersed liquid crystal (H-PDLC) transmission grating. The light-induced refractive- index modulation for neutrons is about 10-6, i.e., nearly two orders of magnitude larger than in the best photo-neutronrefractive materials probed up to now. This makes H-PDLCs a promising candidate for fabricating neutron optical devices.