Continuous Hahn polynomials have surfaced in a number of somewhat obscure physical applications. For example, they have emerged in the description of two-photon processes in hydrogen, hard-hexagon statistical mechanical models, and Clebsch–Gordan expansions for unitary representations of the Lorentz group SO(3,1). In this paper it is shown that there is a simple and elegant way to construct these polynomials using the Heisenberg algebra.