By searching for the Zeeman effect in 21 cm H I spectra taken at 52 positions across the face of the Ophiuchus dark cloud complex, we have mapped out the strength of the line-of-sight magnetic field in the atomic gas associated with the complex. The H I line profiles are comprised of multiple components, which are identified as arising from different physical regimes along the line of sight. A technique known as ''Gaussianizing'' is used to fit an independent field strength to each velocity component in each spectrum. The components with LSR velocities closest to the molecular gas in Ophiuchus are typically seen in self-absorption, as is to be expected if the H I giving rise to this component is indeed associated with relatively cold (i.e., molecular) gas. Thus, we take the field in the self-absorption component of the H I to be most representative of the dark cloud complex. Using the line-of-sight field strengths measured via detection of the Zeeman effect in the H I self-absorption component, and optical polarization data which describe the plane-of-the-sky field structure, we present a model for the three-dimensional structure of the magnetic field near L1688. We estimate the mean uniform field for this region to be 10.2 muG, with an inclination to the line-of-sight of 32-degrees. If there are four correlation lengths of the field along the line of sight, and the fluctuating component of the field is isotropic in three dimensions, then the typical strength of the nonuniform field is approximately 6 muG, and the ratio of energy in the nonuniform and uniform field is of order unity. By comparing the line widths and Alfven speeds for the positions where the Zeeman effect is detected in a self-absorption component, we find rough equality between kinetic and magnetic energy if the gas density in the region producing the H I self-absorption averages approximately 40 cm-3.