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 17Equation or symbol description not available MJ and 14Equation or symbol description not available 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.