Optical activity measurements have been performed on the smectic blue phases (BPSm), which are a new kind of chiral liquid crystal. BPSm exhibit both three-dimensional orientational order, like the classical blue phases, and smectic positional order. Thus, they can be viewed as the three-dimensional counterpart of the twist grain boundary phases. A comparison with the optical activity of the classical blue phases is carried out, and an estimation of the BP Sm lattice parameter is reported for the first time.