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We present the discovery of a planetary-mass companion to CFHTWIR-Oph 98, a low-mass brown dwarf member of the young Ophiuchus star-forming region, with a wide 200-au separation (1.46 arcsec). The companion was identified using Hubble Space Telescope images, and confirmed to share common proper motion with the primary using archival and new ground-based observations. Based on the very low probability of the components being unrelated Ophiuchus members, we conclude that Oph 98 AB forms a binary system. From our multi-band photometry, we constrain the primary to be an M9-L1 dwarf, and the faint companion to have an L2-L6 spectral type. For a median age of 3 Myr for Ophiuchus, fits of evolutionary models to measured luminosities yield masses of $15.4\pm0.8$ M$_\mathrm{Jup}$ for Oph 98 A and $7.8\pm0.8$ M$_\mathrm{Jup}$ for Oph 98 B, with respective effective temperatures of $2320\pm40$ K and $1800\pm40$ K. For possible system ages of 1-7 Myr, masses could range from 9.6-18.4 M$_\mathrm{Jup}$ for the primary, and from 4.1-11.6 M$_\mathrm{Jup}$ for the secondary. The low component masses and very large separation make this binary the lowest binding energy system imaged to date, indicating that the outcome of low-mass star formation can result in such extreme, weakly-bound systems. With such a young age, Oph 98 AB extends the growing population of young free-floating planetary-mass objects, offering a new benchmark to refine formation theories at the lowest masses.