  Recent observations, particularly from the HESS Collaboration, have revealed
rich Galactic populations of TeV gamma-ray sources, including a collection
unseen in other wavelengths. Many of these gamma-ray spectra are well measured
up to ~10 TeV, where low statistics make observations by air Cerenkov
telescopes difficult. To understand these mysterious sources, especially at
much higher energies--where a cutoff should eventually appear--new techniques
are needed. We point out the following: (1) For a number of sources, it is very
likely that pions, and hence TeV neutrinos, are produced; (2) As a general
point, neutrinos should be a better probe of the highest energies than gamma
rays, due to increasing detector efficiency; and (3) For several specific
sources, the detection prospects for km^3 neutrino telescopes are very good,
about 1-10 events/year, with low atmospheric neutrino background rates above
reasonable energy thresholds. Such signal rates, as small as they may seem,
will allow neutrino telescopes to powerfully discriminate between models for
the Galactic TeV sources, with important consequences for our understanding of
cosmic-ray production.
