We show how to realize a single-photon Dicke state in a large one-dimensional array of two-level systems, and discuss how to test its quantum properties. The realization of single-photon Dicke states relies on the cooperative nature of the interaction between a field reservoir and an array of two-level-emitters. The resulting dynamics of the delocalized state can display Rabi-like oscillations when the number of two-level emitters exceeds several hundred. In this case, the large array of emitters is essentially behaving like a "mirror-less cavity". We outline how this might be realized using a multiple-quantum-well structure or a dc-SQUID array coupled to a transmission line, and discuss how the quantum nature of these oscillations could be tested with an extension of the Leggett-Garg inequality.