  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 (NMR), 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 NMR $T_1^{-1}$ relaxation rate
data in the (13 $\pm$ 1)% Br-doped DTN, is found to be in excellent agreement
with the theoretical prediction from large-scale quantum Monte Carlo
simulations.
