  We present a method for simulating the evolution of HII regions driven by
point sources of ionizing radiation in magnetohydrodynamic media, implemented
in the three-dimensional Athena MHD code. We compare simulations using our
algorithm to analytic solutions and show that the method passes rigorous tests
of accuracy and convergence. The tests reveal several conditions that an
ionizing radiation-hydrodynamic code must satisfy to reproduce analytic
solutions. As a demonstration of our new method, we present the first
three-dimensional, global simulation of an HII region expanding into a
magnetized gas. The simulation shows that magnetic fields suppress sweeping up
of gas perpendicular to magnetic field lines, leading to small density
contrasts and extremely weak shocks at the leading edge of the HII region's
expanding shell.
