We imaged five objects near the star-forming clouds of Ophiuchus with the Keck Laser Guide Star AO system. We resolved sources 11 (Oph 16222-2405) and 16 (Oph 16233-2402) from Allers and coworkers into binary systems. Source 11 is resolved into a 243 AU binary, the widest known for a very low mass (VLM) binary. The binary nature of source 11 was discovered first by Allers and independently here, during which we obtained the first spatially resolved R ~ 2000 near-infrared (J and K) spectra, mid-IR photometry, and orbital motion estimates. We estimate for 11A and 11B gravities (log g > 3.75), ages (5 ± 2 Myr), luminosities [log(L/L☉) = -2.77 ± 0.10 and -2.96 ± 0.10], and temperatures (Teff = 2375 ± 175 K and 2175 ± 175 K). We find self-consistent DUSTY evolutionary model (Chabrier and coworkers) masses of 17 MJ and 14 MJ, for 11A and 11B, respectively. Our masses are higher than those previously reported (13-15 MJ and 7-8 MJ) by Jayawardhana & Ivanov. Hence, we find that the system is unlikely a "planetary mass binary," as do Luhman and coworkers, but it has the second lowest mass and lowest binding energy of any known binary. Oph 11 and Oph 16 belong to a newly recognized population of wide (≳100 AU), young (<10 Myr), roughly equal mass, VLM stellar and brown dwarf binaries. We deduce that ~6% ± 3% of young (<10 Myr) VLM objects are in such wide systems. However, only 0.3% ± 0.1% of old field VLM objects are found in such wide systems. Thus, young, wide, VLM binary populations may be evaporating, due to stellar encounters in their natal clusters, leading to a field population depleted in wide VLM systems.