  We perform a lattice Monte-Carlo calculation of the two-point functions of
the energy-momentum tensor at finite temperature in the SU(3) gauge theory.
Unprecedented precision is obtained thanks to a multi-level algorithm. The
lattice operators are renormalized non-perturbatively and the classical
discretization errors affecting the correlators are corrected for. A robust
upper bound for the shear viscosity to entropy density ratio is derived, eta/s
< 1.0, and our best estimate is eta/s = 0.134(33) at T=1.65Tc under the
assumption of smoothness of the spectral function in the low-frequency region.
