  We consider models of inflation in supergravity with a shift symmetry. We
focus on models with one moduli and one inflaton field. The presence of this
symmetry guarantees the existence of a flat direction for the inflaton field.
Mildly breaking the shift symmetry using a superpotential which depends not
only on the moduli but also on the inflaton field allows one to lift the
inflaton flat direction. Along the inflaton direction, the eta-problem is
alleviated. Combining the KKLT mechanism for moduli stabilization and a shift
symmetry breaking superpotential of the chaotic inflation type, we find models
reminiscent of ``mutated hybrid inflation'' where the inflationary trajectory
is curved in the moduli--inflaton plane. We analyze the phenomenology of these
models and stress their differences with both chaotic and hybrid inflation.
