  We report on the attainment of a degenerate Fermi gas of $\rm^{6}Li$ in
contact with a Bose-Einstein condensate (BEC) of $^{84}$Sr. A degeneracy of
$T/T_F=0.33(3)$ is observed with $1.6\times10^5$ $^{6}$Li atoms in the two
lowest energy hyperfine states together with an almost pure BEC of
$3.1\times10^5$ $^{84}$Sr atoms. The elastic s-wave scattering length between
$^6$Li and $^{84}$Sr is estimated to be
$|a_{\rm^{6}Li-\rm^{84}Sr}|=(7.1_{-1.7}^{+2.6})a_0$ ($a_0$ being the Bohr
radius) from measured interspecies thermalization rates in an optical dipole
trap.
