The autocorrelation between two members of a galaxy population is symmetric under the interchange of the two galaxies being correlated. The cross-correlation between two different types of galaxies, separated by a vector r, is not necessarily the same as that for a pair separated by -r. Local anisotropies in the two-point cross-correlation function may thus indicate a specific direction which when mapped as a function of position trace out a vector field. This vector field can then be decomposed into longitudinal and transverse components, and those transverse components written as positive- and negative-helicity components. A locally asymmetric cross-correlation of the longitudinal type arises naturally in halo clustering, even with Gaussian initial conditions, and could be enhanced with local-type non-Gaussianity. Early-Universe scenarios that introduce a vector field may also give rise to such effects. These antisymmetric cross-correlations also provide a new possibility to seek a preferred cosmic direction correlated with the hemispherical power asymmetry in the cosmic microwave background and to seek a preferred location associated with the cosmic microwave background cold spot. New ways to seek cosmic parity breaking are also possible.