  The H3O+ molecule probes the oxygen chemistry and the ionization rate of
dense circumnuclear gas in galaxies. In particular, recent H3O+ observations
show variations in the cosmic-ray ionization rate by factors of $>$10 within
our Galaxy. Using the JCMT, we have observed the 364 GHz line of p-H3O+ in the
centers of M82 and Arp 220. In Arp 220, the line profile suggests that the
emission originates in the Western nucleus. In M82, both the eastern molecular
peak and the circumnuclear region contribute to the emission. The derived
column densities, abundances, and H3O+ / H2O ratios indicate ionization rates
similar to or even exceeding that in the Galactic Center. Model calculations of
the chemistry of irradiated molecular gas indicate a likely origin of this high
ionization rate in the extended, evolved starburst of M82. In contrast,
irradiation by X-rays from the AGN disk is the most likely model for Arp 220.
