  By solving the time-dependent radiation transfer problem of stellar radiation
through evolving superbubbles within a smoothly varying HI distribution, we
estimate the fraction of ionizing photons emitted by OB associations that
escapes the HI disk of our Galaxy into the halo and intergalactic medium (IGM).
We consider both coeval star-formation and a Gaussian star-formation history
with a time spread sigma_t = 2 Myr. We consider both a uniform H I distribution
and a two-phase (cloud/intercloud) model, with a negligible filling factor of
hot gas. We find that the shells of the expanding superbubbles quickly trap or
attenuate the ionizing flux, so that most of the escaping radiation escapes
shortly after the formation of the superbubble. For the coeval star-formation
history, the total fraction of Lyman Continuum photons that escape both sides
of the disk in the solar vicinity is f_esc approx 0.15 +/- 0.05. For the
Gaussian star formation history, f_esc approx 0.06 +/- 0.03, a value roughly a
factor of two lower than the results of Dove & Shull (1994), where superbubbles
were not considered. For a local production rate of ionizing photons Psi_LyC =
4.95 X 10^7 cm^{-2} s^{-1}, the flux escaping the disk is Phi_LyC approx
(1.5-3.0) X 10^6 cm^{-2} s^{-1} for coeval and Gaussian star formation,
comparable to the flux required to sustain the Reynolds layer.
