and measurement. The realization of such a detector has been complicated by the fact that photon- photon interactions are very weak at optical frequencies. At microwave frequencies, very strong photon-photon interactions have been demonstrated. Here however, the single-photon detector has been elusive due to the low energy of the microwave photon. In this article, we present a realistic proposal for quantum nondemolition measurements of a single propagating microwave photon. The detector design is built on a of chain of artificial atoms connected through circulators which break time-reversal symmetry, making both signal and probe photons propagate in one direction only. Our analysis is based on the theory of cascaded quantum systems and quantum trajectories which takes the full dynamics of the atom-field interaction into account. We show that a signal-to-noise ratio above one can be realized with current state of the art microwave technology.