  We report on the realization of a stable mixture of ultracold lithium and
ytterbium atoms confined in a far-off-resonance optical dipole trap. We observe
sympathetic cooling of 6Li by 174Yb and extract the s-wave scattering length
magnitude |a6Li-174Yb| = (13 \pm 3)a0 from the rate of inter-species
thermalization. Using forced evaporative cooling of 174Yb, we achieve reduction
of the 6Li temperature to below the Fermi temperature, purely through
inter-species sympathetic cooling.
