Single-layer transition metal dichalcogenides are at the center of an ever increasing research effort both in terms of fundamental physics and applications. Exciton-phonon coupling plays a key role in determining the (opto)electronic properties of these materials. However, the exciton-phonon coupling strength has not been measured at room temperature. Here, we use two-dimensional micro-spectroscopy to determine exciton-phonon coupling of single-layer MoSe2. We detect beating signals as a function of waiting time induced by the coupling between A excitons and A'1 optical phonons. Analysis of beating maps combined with simulations provides the exciton-phonon coupling. We get a Huang-Rhys factor ~1, larger than in most other inorganic semiconductor nanostructures. Our technique offers a unique tool to measure exciton-phonon coupling also in other heterogeneous semiconducting systems, with a spatial resolution ~260 nm, and provides design-relevant parameters for the development of optoelectronic devices.