  We present new optical imaging and spectroscopy and HI spectral line imaging
of the dwarf galaxy ADBS 113845+2008 (hereafter ADBS 1138). This metal-poor
(Z~30% Z_Sun), "post-starburst" system has one of the most compact stellar
distributions known in any galaxy to date (B-band exponential scale length
=0.57 kpc). In stark contrast to the compact stellar component, the neutral gas
is extremely extended; HI is detected to a radial distance of ~25 kpc at the
10^19 cm^-2 level (>44 B-band scale lengths). Comparing to measurements of
similar "giant disk" dwarf galaxies in the literature, ADBS 1138 has the
largest known HI-to-optical size ratio. The stellar component is located near
the center of a broken ring of HI that is ~15 kpc in diameter; column densities
peak in this structure at the ~3.5x10^20 cm^-2 level. At the center of this
ring, in a region of comparatively low HI column density, we find ongoing star
formation traced by H alpha emission. We sample the rotation curve to the point
of turn over; this constrains the size of the dark matter halo of the galaxy,
which outweighs the luminous component (stars + gas) by at least a factor of
15. To explain these enigmatic properties, we examine "inside-out" and
"outside-in" evolutionary scenarios. Calculations of star formation energetics
indicate that "feedback" from concentrated star formation is not capable of
producing the ring structure; we posit that this is a system where the large HI
disk is evolving in quiescent isolation. In a global sense, this system is
exceedingly inefficient at converting neutral gas into stars.
