  We construct N=1 supergravity extensions of scalar field theories with
higher-derivative kinetic terms. Special attention is paid to the auxiliary
fields, whose elimination leads not only to corrections to the kinetic terms,
but to new expressions for the potential energy as well. For example, a
potential energy can be generated even in the absence of a superpotential. Our
formalism allows one to write a supergravity extension of any higher-derivative
scalar field theory and, therefore, has applications to both particle physics
and cosmological model building. As an illustration, we couple the
higher-derivative DBI action describing a 3-brane in 6-dimensions to N=1
supergravity. This displays a number of new features-- including the fact that,
in the regime where the higher-derivative kinetic terms become important, the
potential tends to be everywhere negative.
