We present a general approach to analyzing the optical activity of semiconductor nanocrystals of chiral shapes. By using a coordinate transformation that turns a chiral nanocrystal into a nanocuboid, we calculate the rotatory strengths, dissymmetry factors, and peak values of the circular dichroism (CD) signal upon intraband transitions inside the nanocrystal. It is shown that the atomic roughness of the nanocrystal surface can result in rotatory strengths as high as 10-36 erg×cm3 and in peak CD signals of about 0.1 cm-1 for typical nanocrystal densities of 1016 cm-3. The developed approach may prove useful for other nanocrystal shapes whereas the derived expressions apply directly for the modeling and interpretation of experimental CD spectra of quantum dots, nanorods, and nanoplatelets.