  We report the simultaneous production of Bose-Einstein condensates (BECs) of
$^{87}$Rb and $^{133}$Cs atoms in separate optical traps. The two samples are
mixed during laser cooling and loading but are separated by $400 \mu$m for the
final stage of evaporative cooling. This is done to avoid considerable
interspecies three-body recombination, which causes heating and evaporative
loss. We characterize the BEC production process, discuss limitations, and
outline the use of the dual-species BEC in future experiments to produce
rovibronic ground state molecules, including a scheme facilitated by the
superfluid-to-Mott-insulator (SF-MI) phase transition.
