We present results on the photorefractive properties of chiral smectic A liquid-crystal phases dispersed in cylindrical cavities in a photoconducting polymer. The refractive-index modulation is due to the electroclinic effect, which is linear in the electric field, in contrast with the effect that is due to the dielectric anisotropy that is typical of nematic phases. We obtained grating buildup times of ~25 ms , limited by the speed of the space-charge field formation in the photoconducting matrix.