  We report on the creation of dual-species Bose-Einstein condensates (BECs) of
$^{23}$Na atoms and $^{133}$Cs atoms. We demonstrate sympathetic cooling of Cs
with Na in a magnetic quadrupole trap and a crossed optical dipole trap,
leading to Na BECs with $8 \times 10^5$ atoms and Cs BECs with $3.5 \times
10^4$ atoms. Investigating cross-thermalization and lifetimes of the mixture,
we find that the Na and Cs BECs are miscible and overlapping, interacting with
a moderate interspecies scattering length of $18(4)\,a_0$ at $23\,$G and
$29(4)\,a_0$ at $894\,$G and coexisting for tens of seconds. Overlapping
condensates of Na and Cs offer new possibilities for many-body physics with
ultracold bosonic mixtures and constitute an ideal starting point for the
creation of ultracold ensembles of NaCs ground state molecules.
