Linearly polarized, nonmasing, rotational lines have been detected for the
first time in the interstellar medium. This effect occurs in molecular clou
ds with a magnetic field and traces the field direction, offering an altern
ative technique to dust emission polarimetry. The line polarization mechani
sm is similar to that in masers, but with lower degrees of polarization (si
milar to 1%). We have detected the effect toward the Galactic center and it
s surrounding "2 pc ring" and in the molecular clouds S140 and DR 21 (tenta
tively), in the lines CO J = 2-1 and J = 3-2 and (CO)-C-13 J = 2-1. The ded
uced magnetic field directions agree well with previous dust polarimetry re
sults, confirming that the line polarization is a real effect. This new tec
hnique will be useful in sources that are too Faint fur dust polarimetry an
d can also be used to investigate the three-dimensional morphology of magne
tic fields in cases in which the velocity structure of the clouds is known.