The Heisenberg category H is a monoidal category defined by Khovanov using representation theory of symmetric groups (a deformation H_q was given by Licata and Savage using Hecke algebras). Both H and H_q categorify the Heisenberg algebra. The Hochschild homology (or, trace) of H_q is an algebra, and we show it is a specialization of the elliptic Hall algebra E. In this setting, the action of E on symmetric functions comes from a 2-representation of H_q defined using Hecke algebras. (This is joint work with Cautis, Lauda, Licata, and Sussan.)