D-term hybrid inflation is a simple, attractive particle physics framework for realizing inflation. It is however plagued by two serious problems: First, a crucial ingredient of the model is a Fayet-Iliopoulos (FI) term, whose embedding into a UV complete theory raises serious conceptual problems. Second, D-term hybrid inflation produces cosmic strings with a large string tension, in contradiction to the results of CMB experiments. In this talk, I demonstrate how both of these problems can be simultaneously overcome by a dynamically generated FI-term. The resulting D-term inflation model provides an excellent fit to the current CMB data. I furthermore present a new regime of the model, allowing for a large amount of e-folds of inflation after the critical point. In this regime, a period of `chaotic inflation' with a sizable tensor-to-scalar ratio naturally arises from the decay of a false vacuum of GUT-scale energy.