Small-angle diffraction of polarized neutrons and resonant contribution to diffraction of synchrotron radiation have been applied to prove chirality of the crystal and magnetic structures of the magnetoelectric insulator Cu₂OSeO₃. Similarly to other chiral magnets with P2₁3 crystal structure the corresponding chiralities are linked to each other via the phenomenological Dzyaloshinskii-Moriya interaction. The crystal and magnetic structures for Cu₂OSeO₃ have the same chirality as is observed for MnSi, Mn_1-xFe_xSi, and MnGe. However, the combination of chiralities is opposite to that proposed from a recent theoretical consideration. The chiral link between structure and magnetism previously found for metallic compounds is also proved to exist for an insulator (Cu₂OSeO₃), allowing us to conclude that the conducting electrons play no role in a possible common microscopic mechanism of this specific magnetolattice interaction.