  We present the first ab initio determination of the shear viscosity eta of
the Unitary Fermi Gas, based on finite temperature quantum Monte Carlo
calculations and the Kubo linear-response formalism. We determine the
temperature dependence of the shear viscosity to entropy density ratio eta/s.
The minimum of eta/s appears to be located above the critical temperature for
the superfluid-to-normal phase transition with the most probable value being
eta/s approx 0.2 hbar/kB, which almost saturates the Kovtun-Son-Starinets
universal value hbar/(4 pi kB).
