  Although there is strong theoretical and experimental evidence for
electron-hole superfluidity in separated sheets of electrons and holes at low
$T$, extending superfluidity to high $T$ is limited by strong 2D fluctuations
and Kosterlitz-Thouless effects. We show this limitation can be overcome using
a superlattice of alternating electron- and hole-doped semiconductor
monolayers. The superfluid transition in a 3D superlattice is not topological,
and for strong electron-hole pair coupling, the transition temperature $T_c$
can be at room temperature. As a quantitative illustration, we show $T_c$ can
reach $270$ K for a superfluid in a realistic superlattice of transition metal
dichalcogenide monolayers.
