  We study hydrodynamic fluctuations in a non-relativistic fluid. We show that
in three dimensions fluctuations lead to a minimum in the shear viscosity to
entropy density ratio $\eta/s$ as a function of the temperature. The minimum
provides a bound on $\eta/s$ which is independent of the conjectured bound in
string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy
density. For the dilute Fermi gas at unitarity we find $\eta/s\gsim 0.2\hbar$.
This bound is not universal -- it depends on thermodynamic properties of the
unitary Fermi gas, and on empirical information about the range of validity of
hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic
mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear
viscosity in two dimensions diverges as $\log(1/ \omega)$.
