We report the first interferometric detection and mapping of linearly polar
ized spectral line emission due to the Goldreich-Kylafis effect. Our polari
zation maps of the CO J = 2 --> 1 Line in the molecular outflow powered by
the very young stellar system NGC 1333 IRAS 4A make it possible to define t
he direction of the magnetic field in the outflow. Comparison with theoreti
cal predictions implies that the magnetic field is parallel to the polariza
tion. Our data suggest that the deflection of the outflow may be the result
of the interaction between the outflow and the magnetic field. We also det
ect and map the linearly polarized dust continuum emission at 1.3 mm. The p
olarization map of the dust continuum is roughly consistent with an hourgla
ss magnetic field morphology; i.e., it is in agreement with theoretical mod
els of interstellar cloud contraction with a frozen-in magnetic field. The
two techniques for mapping magnetic field morphologies agree. In general, t
he two techniques sample different column densities, and together they allo
w the study of magnetic field morphology over wider areas than either techn
ique by itself would permit.