Using a novel, overdamped, oscillator flown aboard the space shuttle, we me
asured the viscosity of xenon near the liquid-vapor critical point in the f
requency range 2 Hz less than or equal to f less than or equal to 12 Hz. Th
e measured viscosity divergence is characterized by the exponent z(eta) = 0
.0690 +/- 0.0006, in agreement with the value z(eta) = 0.067 +/- 0.002 calc
ulated from a two-loop perturbation expansion. Viscoelastic behavior was ev
ident when t = (T - T-c)/T-c < 10(-5) and dominant when t < 10(-6), further
from T-c than predicted. Viscoelastic behavior scales as Af tau where tau
is the fluctuation decay time. The measured value of A is 2.0 +/- 0.3 times
the result of a one-loop calculation. (Uncertainties stated are one standa
rd uncertainty.).