This work calculates the first correction to the leading order q\={q}
dilepton production rates due to shear viscosity in an expanding gas. The
modified rates are integrated over the space-time history of a viscous
hydrodynamic simulation of RHIC collisions. The net result is a {\em hardening}
of q⊥ spectrum with the magnitude of the correction increasing with
invariant mass. We argue that a thermal description is reliable for invariant
masses less than Mmax≈(2τ0T02)/(η/s). For reasonable
values of the shear viscosity and thermalization time Mmax≈4.5 GeV.
Finally, the early emission from a viscous medium is compared to emission from
a longitudinally free streaming plasma. Qualitative differences in q⊥
spectrum are seen which could be used to extract information on the
thermalization time, viscosity to entropy ratio and possibly the thermalization
mechanism in heavy-ion collisions.Comment: 17 pages, 8 figure