  We report the formation of a dual-species Bose-Einstein condensate of
$^{87}$Rb and $^{133}$Cs in the same trapping potential. Our method exploits
the efficient sympathetic cooling of $^{133}$Cs via elastic collisions with
$^{87}$Rb, initially in a magnetic quadrupole trap and subsequently in a
levitated optical trap. The two condensates each contain up to $2\times10^{4}$
atoms and exhibit a striking phase separation, revealing the mixture to be
immiscible due to strong repulsive interspecies interactions. Sacrificing all
the $^{87}$Rb during the cooling, we create single species $^{133}$Cs
condensates of up to $6\times10^{4}$ atoms.
