Supersymmetric inflation with the ordinary Higgs?

We consider a model of D-term inflation in which the inflaton coincides with the standard Higgs doublet. Non-renormalizable terms are controlled by a discrete R-symmetry of the superpotential. We consider radiative corrections to the scalar potential and find that Higgs inflation in the slow-roll approximation is viable and consistent with CMB data, although with a rather large value of the non-renormalizable coupling involved.