We report strong diffraction of cold neutrons from an only 30 micro m 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 2 orders of magnitude larger than in the best photo-neutron-refractive materials probed up to now. This makes H-PDLCs a promising candidate for fabricating neutron-optical devices.