  We have produced a quantum degenerate mixture of fermionic alkali 6Li and
bosonic spin-singlet 174Yb gases. This was achieved using sympathetic cooling
of lithium atoms by evaporatively cooled ytterbium atoms in a far-off-resonant
optical dipole trap. We observe co-existence of Bose condensed (T/T_c~0.8)
174Yb with 2.3*10^4 atoms and Fermi degenerate (T/T_F~0.3) 6Li with 1.2*10^4
atoms. Quasipure Bose-Einstein condensates of up to 3*10^4 174Yb atoms can be
produced in single-species experiments. Our results mark a significant step
toward studies of few and many-body physics with mixtures of alkali and
alkaline-earth-like atoms, and for the production of paramagnetic polar
molecules in the quantum regime. Our methods also establish a convenient scheme
for producing quantum degenerate ytterbium atoms in a 1064nm optical dipole
trap.
