We treat polymer chains with an intrinsic curvature, which we model by a continuum extension of a microscopic model with preferred bending angle. From this model, we obtain a modified form of the mean-field Hamiltonian used to describe semiflexible chains. We then employ an auxiliary field operator to enforce the mean curvature constraint along with a torsional constraint. Using this formalism, we provide analytic results for the tangent-tangent correlator [u( s).u(s')], mean square radius of gyration [S-2], and mean square separation [R-2]. We also obtain approximate results for the force-extension behavior of these chains, and discuss possible extensions to curved polymers with excluded volume and other self-interactions.