  We propose the angular distribution of lepton pairs produced in
ultrarelativistic heavy-ion collisions as a probe of thermalization of the
quark-gluon plasma. We focus on dileptons with invariant masses large enough
that they are produced through quark-antiquark annihilation in the early stages
of the collision. The angular distribution of the lepton in the rest frame of
the pair then reflects the angular distribution of quark momenta. At early
times, the transverse pressure of the quark-gluon plasma is larger than its
longitudinal pressure as a result of the fast longitudinal expansion, which
results in an oblate lepton distribution. By contrast, direct (Drell-Yan)
production by quarks and antiquarks from incoming nuclei, whose momenta are
essentially longitudinal, results in a prolate distribution. As the invariant
mass increases, Drell-Yan gradually becomes the dominant source of dilepton
production, and the lepton distribution evolves from oblate to prolate. The
invariant mass at which the transition occurs is highly sensitive to the
equilibration time of the quark-gluon plasma or, equivalently, the shear
viscosity over entropy ratio $\eta/s$ in the early stages of the collision.
