It is generally agreed upon that the Milky Way has spiral arms but their number and nature are still under debate. The spiral arms are thought to be either quasi-stationary density waves or transient arms that quickly form, wind up, and dissipate. These two models of spiral structure make qualitatively different predictions for the velocity fields of the gaseous spiral arms. To determine which model applies to the Milky Way, we have mapped the velocity field of interstellar gas and dust as a function of location in the Galactic plane. These maps are inconsistent with simulations of quasi-stationary density wave spiral structure and consistent with simulations of transient spiral structure.