For centuries mankind has been modifying the optical properties of materials: first, by elaborating the geometry and composition of structures made of materials found in nature, later by structuring the existing materials at a scale smaller than the operating wavelength. Here we suggest an original approach to introduce optical activity in nanostructured materials, by theoretically demonstrating that conventional achiral semiconducting nanocrystals become optically active in the presence of screw dislocations, which can naturally develop during the nanocrystal growth. We show the new properties to emerge due to the dislocation-induced distortion of the crystal lattice and the associated alteration of the nanocrystal's electronic subsystem, which essentially modifies its interaction with external optical fields. The g-factors of intraband transitions in our nanocrystals are found comparable with dissymmetry factors of chiral plasmonic complexes, and exceeding the typical g-factors of chiral molecules by a factor of 1000. Optically active semiconducting nanocrystals-with chiral properties controllable by the nanocrystal dimensions, morphology, composition and blending ratio-will greatly benefit chemistry, biology and medicine by advancing enantiomeric recognition, sensing and resolution of chiral molecules.