  We study the shear viscosity of a dilute Fermi gas as a function of the
scattering length in the vicinity of the unitarity limit. The calculation is
based on kinetic theory, which provides a systematic approach to transport
properties in the limit in which the fugacity $z=n\lambda^3/2$ is small. Here,
$n$ is the density of the gas and $\lambda$ is the thermal wave length of the
fermions. At leading order in the fugacity expansion the shear viscosity is
independent of density, and the minimum shear viscosity is achieved at
unitarity. At the next order medium effects modify the scattering amplitude as
well as the quasi-particle energy and velocity. We show that these effects
shift the minimum of the shear viscosity to the Bose-Einstein condensation
(BEC) side of the resonance, in agreement with the result of recent
experiments.
