We have serendipitously detected a strong O VI-bearing Lyman limit system at z_abs = 0.3558 toward the QSO J1009+0713 (z_em = 0.456) in our survey of low-redshift galaxy halos with the Hubble Space Telescopes Cosmic Origins Spectrograph. Its rest-fra
me equivalent width of W_r = 835 +/- 49 mA is the highest for an intervening absorber yet detected in any low-redshift QSO sightline, with absorption spanning 400 km s^-1 in its rest frame. HST/WFC3 images of the galaxy field show that the absorber is associated with two galaxies lying at 14 and 46 kpc from the QSO line of sight. The bulk of the absorbing gas traced by H I resides in two strong, blended component groups that possess a total logN(HI) = 18 - 18.8. The ion ratios and column densities of C, N, O, Mg, Si, S, and Fe, except the O VI, can be accommodated into a simple photoionization model in which diffuse, low-metallicity halo gas is exposed to a photoionizing field from stars in the nearby galaxies that propagates into the halo at 10% efficiency. We constrain the metallicity firmly within the range 0.1 - 1 Zsun, and photoionization modeling indirectly indicates a subsolar metallicity of 0.05 - 0.5 Zsun. The appearance of strong O VI and nine Mg II components and our review of similar systems in the literature support the interface picture of high-velocity O VI: the total strength of the O VI shows a positive correlation with the number of detected components in the low-ionization gas, however the total O VI column densities still far exceed the values expected from interface models for the number of detected clouds.
