We demonstrate the generation of a coherent water window x ray by extending the plateau region of high-order harmonics under a neutral-medium condition. The maximum harmonic photon energies attained are 300 and 450 eV in Ne and He, respectively. Our proposed generation scheme, combining a 1.6 microm laser driver and a neutral Ne gas medium, is efficient and scalable in output yields of the water window x ray. Thus, the precept of the design parameter for a single-shot live-cell imaging by contact microscopy is presented.