We present a hadronic model of activity for galactic γ-ray-loud binaries, in which the multi-TeV neutrino flux from the source can be much higher and/or harder than the detected TeV γ-ray flux. This is related to the fact that most neutrinos are produced in proton-proton interactions close to the bright massive star, in a region optically thick for the TeV γ rays. Considering the specific example of LS I+61°303, we derive upper bounds for neutrino fluxes from various proton injection spectra compatible with the observed multiwavelength spectrum. At this upper level of neutrino emission, we demonstrate that ICECUBE will not only detect this source at 5σ C.L. after one year of operation, but, after three years of exposure, will also collect a sample marginally sufficient to constrain the spectral characteristics of the neutrino signal, directly related to the underlying source acceleration mechanisms. © 2009 The American Physical Society.