We present the results of dust emission polarization measurements of Ophiuchus-B (Oph-B) carried out using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) camera with its associated polarimeter (POL-2) on the James Clerk Maxwell Telescope in Hawaii. This work is part of the B-fields in Star-forming Region Observations survey initiated to understand the role of magnetic fields in star formation for nearby star-forming molecular clouds. We present a first look at the geometry and strength of magnetic fields in Oph-B. The field geometry is traced over ∼0.2 pc, with clear detection of both of the sub-clumps of Oph-B. The field pattern appears significantly disordered in sub-clump Oph-B1. The field geometry in Oph-B2 is more ordered, with a tendency to be along the major axis of the clump, parallel to the filamentary structure within which it lies. The degree of polarization decreases systematically toward the dense core material in the two sub-clumps. The field lines in the lower density material along the periphery are smoothly joined to the large-scale magnetic fields probed by NIR polarization observations. We estimated a magnetic field strength of 630 ± 410 μG in the Oph-B2 sub-clump using a Davis-Chandrasekhar-Fermi analysis. With this magnetic field strength, we find a mass-to-flux ratio λ = 1.6 ± 1.1, which suggests that the Oph-B2 clump is slightly magnetically supercritical.