  We present the first resolved study of the radio continuum properties of I Zw
18, the dwarf galaxy with the lowest known nebular metal abundance in the local
universe. New Very Large Array radio continuum images at 20 and 3.6 cm are
compared to various Hubble Space Telescope images, and we find a striking
morphological similarity between high-resolution H alpha and short wavelength
radio continuum emission, especially in the H alpha shell in the northwest
region. We separate thermal and nonthermal components of the emission, and find
a large synchrotron halo surrounding the galaxy. Comparison between H alpha and
X-band fluxes suggests that the emission at 3.6 cm is dominated by thermal
processes; an additional synchrotron component dominates the flux at 20 cm and
produces a modest fraction of the detected flux at 3.6 cm. The fluxes of three
of the four major emission peaks show a mix of thermal and nonthermal
processes, while one shows a nearly flat spectral index. The strong synchrotron
component argues for active star formation throughout the disk for at least the
last ~ 30 Myr. These sensitive observations provide a new, detailed view of the
nature of radio continuum emission in the very low metallicity interstellar
medium. Comparing with the literature, the role of metallicity in the evolution
of radio continuum emission seems to be secondary to other factors such as the
recent star formation history and the presence or absence of outflows from star
formation regions.
