  Gravitational lensing introduces the possibility of multiple (macroscopic)
paths from an astrophysical neutrino source to a detector. Such a multiplicity
of paths can allow for quantum mechanical interference to take place that is
qualitatively different to neutrino oscillations in flat space. After an
illustrative example clarifying some under-appreciated subtleties of the phase
calculation, we derive the form of the quantum mechanical phase for a neutrino
mass eigenstate propagating non-radially through a Schwarzschild metric. We
subsequently determine the form of the interference pattern seen at a detector.
We show that the neutrino signal from a supernova could exhibit the
interference effects we discuss were it lensed by an object in a suitable mass
range. We finally conclude, however, that -- given current neutrino detector
technology -- the probability of such lensing occurring for a
(neutrino-detectable) supernova is tiny in the immediate future.
