Single-stranded DNA chains enable postsynthesis sorting of single-walled carbon D-DNA nanotubes (CNTs) according to their diameter and helicity by wrapping helically around CNT surfaces. Both DNA chains and CNTs in these CNT-DNA conjugates are intrinsically chiral. Using a single-stranded DNA chain in both of its chiral realizations, we systematically study cross-chiral interactions between DNA and CNTs by varying the helicity of CNTs within a relatively narrow range of diameters. We find that regardless of the helicity or handedness of the carbon nanotube, the chirality of DNA dictates the handedness of its predominant helical wrap around carbon nanotubes.