  The spontaneous polarization of epitaxial BaTiO$_3$/SrTiO$_3$ superlattices
is studied as a function of composition using first-principles density
functional theory within the local density approximation. With the in-plane
lattice parameter fixed to that of bulk SrTiO$_3$, the computed superlattice
polarization is enhanced above that of bulk BaTiO$_3$ for superlattices with
BaTiO$_3$ fraction larger than 40%. In contrast to their bulk paraelectric
character, the SrTiO$_3$ layers are found to be {\it tetragonal and polar},
possessing nearly the same polarization as the BaTiO$_3$ layers. General
electrostatic arguments elucidate the origin of the polarization in the
SrTiO$_3$ layers, with important implications for other ferroelectric
nanostructures.
