  We present measurements of interspecies thermalization between ultracold
samples of $^{133}$Cs and either $^{174}$Yb or $^{170}$Yb. The two species are
trapped in a far-off-resonance optical dipole trap and $^{133}$Cs is
sympathetically cooled by Yb. We extract effective interspecies thermalization
cross sections by fitting the thermalization measurements to a rate equation
model, giving $\sigma_{\mathrm{Cs^{174}Yb}} = \left(5 \pm 2\right) \times
10^{-13} \, \mathrm{cm^{2}}$ and $\sigma_{\mathrm{Cs^{170}Yb}} = \left(18 \pm
8\right) \times 10^{-13} \, \mathrm{cm^{2}}$. We perform quantum scattering
calculations of the thermalization cross sections and optimize the CsYb
interaction potential to reproduce the measurements. We predict scattering
lengths for all isotopic combinations of Cs and Yb. We also demonstrate the
independent production of $^{174}$Yb and $^{133}$Cs Bose-Einstein condensates
using the same optical dipole trap, an important step towards the realization
of a quantum-degenerate mixture of the two species.
