  Using $\varepsilon$-expansion technique we compute $\eta/s$, where $\eta$ is
the shear viscosity, $s$ is the entropy density, of the normal phase of unitary
Fermi gas in $d=4-\varepsilon$ dimensions to LO in $\varepsilon$. We use
kinetic theory approach and solve transport equations for medium perturbed by a
shear hydrodynamic flow. The collision integrals are calculated to
$\varepsilon^2$ which is LO. The LO result is temperature independent with
$\eta/\rm s\simeq (0.11/\varepsilon^2)(\hbar/k_B).$ The $d=3$ prediction for
$\eta/\rm s$ exceeds the $\hbar/4 \pi k_B$ bound by a factor of about $1.4.$
