The Magellanic Stream and several high-velocity clouds have now been detect
ed in optical line emission. The observed emission measures and kinematics
are most plausibly explained by photoionization due to hot, young stars in
the Galactic disk. The highly favorable orientation of the Stream allows an
unambiguous determination of the fraction of ionizing photons f(esc) which
escape the Galactic disk. We have modeled the production and transport of
ionizing photons through an opaque interstellar medium. Normalization to th
e Stream detections requires f(esc) approximate to 6%, which is in reasonab
le agreement with the flux required to ionize the Reynolds layer. Neither s
hock heating nor emission within a hot Galactic corona can be important in
producing the observed Hat emission. If such a large escape fraction is typ
ical oft, galaxies, star-forming systems dominate the extragalactic ionizin
g background. Within the context of this model, both the three-dimensional
orientation of the Stream and the distances to high-velocity clouds can be
determined by sensitive Ha observations.