In this Letter, we show that the strong coupling between a disordered set of molecular emitters and surface plasmons leads to the formation of spatially coherent hybrid states extended on macroscopic distances. Young-type interferometric experiments performed on a system of J-aggregated dyes spread on a silver layer evidence the coherent emission from different molecular emitters separated by several microns. The coherence is absent in systems in the weak-coupling regime demonstrating the key role of the hybridization of the molecules with the plasmon.