  In an isotropic strongly interacting quantum liquid without quasiparticles,
general scaling arguments imply that the dimensionless ratio $(k_B /\hbar)\,
\eta/s$, where $\eta$ is the shear viscosity and $s$ is the entropy density, is
a universal number. We compute the shear viscosity of the Ising-nematic
critical point of metals in spatial dimension $d=2$ by an expansion below
$d=5/2$. The anisotropy associated with directions parallel and normal to the
Fermi surface leads to a violation of the scaling expectations: $\eta$ scales
in the same manner as a chiral conductivity, and the ratio $\eta/s$ diverges at
low temperature ($T$) as $T^{-2/z}$, where $z$ is the dynamic critical exponent
for fermionic excitations dispersing normal to the Fermi surface.
