Supersymmetric P(X,phi) and the Ghost Condensate

We show how to construct supersymmetric actions for higher-derivative scalar field theories of the form P(X,phi), within the context of d=4, N=1 supersymmetry. This construction is of general use, and is applied to write supersymmetric versions of the Dirac-Born-Infeld action. Our principal application of this formalism is to construct the supersymmetric extension of the ghost condensate. This allows us to study the interplay between supersymmetry, time-dependent backgrounds and violations of the null energy condition.