We formulate a sub-Riemannian X-ray transform on contact manifolds. Such manifolds are modeled locally by 2-step nilpotent Lie groups, with the Heisenberg group exhibiting the simplest case. We explicitly describe the Heisenberg ray transform, and an ongoing attempt at its inversion using tools from noncommutative harmonic analysis that mirror the Euclidean case in the spirit of Helgason.