We present new optical imaging and spectroscopy and H I spectral line imaging of the dwarf galaxy ADBS 113845 + 2008 (hereafter ADBS 1138). This metal-poor (Z ~ 30% Z _☉), "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; H I is detected to a radial distance of ~25 kpc at the 10¹⁹ 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 H I-to-optical size ratio. The stellar component is located near the center of a broken ring of H I that is ~15 kpc in diameter; column densities peak in this structure at the ~3.5 × 10²⁰ cm^–2 level. At the center of this ring, in a region of comparatively low H I column density, we find ongoing star formation traced by Hα 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 H I disk is evolving in quiescent isolation. In a global sense, this system is exceedingly inefficient at converting neutral gas into stars.