We explore the alignment of various achiral liquid crystals on films of aligned double-stranded helical DNA. In all cases and both for the nematic and smectic A phases, we find a distinctly chiral interfacial structure, with the mean orientation of the liquid crystal in contact with the DNA-treated surfaces chirally rotated through a substantial angle with respect to the mean DNA orientation. This rotation originates in the chirality of double-stranded DNA and depends on the liquid crystal molecular structure. We dicuss the role of dipolar and hydrophobic coupling in determining the observed orientation.