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 $2times10^{4}$ 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 $6times10^{4}$ atoms.
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