The coupled spin-1 chains material NiCl_{2}-4SC(NH_{2})_{2} (DTN) doped with Br impurities is expected to be a perfect candidate for observing many-body localization at high magnetic field: the so-called "Bose glass," a zero-temperature bosonic fluid, compressible, gapless, incoherent, and short-range correlated. Using nuclear magnetic resonance, we critically address the stability of the Bose glass in doped DTN, and find that it hosts a novel disorder-induced ordered state of matter, where many-body physics leads to an unexpected resurgence of quantum coherence emerging from localized impurity states. An experimental phase diagram of this new "order-from-disorder" phase, established from nuclear magnetic resonance T_{1}^{-1} relaxation rate data in the 13±1% Br-doped DTN, is found to be in excellent agreement with the theoretical prediction from large-scale quantum Monte Carlo simulations.