By searching for the Zeeman effect in 21 cm H I spectra taken at 52 po
sitions across the face of the Ophiuchus dark cloud complex, we have m
apped out the strength of the line-of-sight magnetic field in the atom
ic gas associated with the complex. The H I line profiles are comprise
d of multiple components, which are identified as arising from differe
nt physical regimes along the line of sight. A technique known as ''Ga
ussianizing'' is used to fit an independent field strength to each vel
ocity component in each spectrum. The components with LSR velocities c
losest to the molecular gas in Ophiuchus are typically seen in self-ab
sorption, as is to be expected if the H I giving rise to this componen
t is indeed associated with relatively cold (i.e., molecular) gas. Thu
s, 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-sigh
t field strengths measured via detection of the Zeeman effect in the H
I self-absorption component, and optical polarization data which desc
ribe the plane-of-the-sky field structure, we present a model for the
three-dimensional structure of the magnetic field near L1688. We estim
ate the mean uniform field for this region to be 10.2 muG, with an inc
lination to the line-of-sight of 32-degrees. If there are four correla
tion lengths of the field along the line of sight, and the fluctuating
component of the field is isotropic in three dimensions, then the typ
ical 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 wher
e the Zeeman effect is detected in a self-absorption component, we fin
d rough equality between kinetic and magnetic energy if the gas densit
y in the region producing the H I self-absorption averages approximate
ly 40 cm-3.