A certain class of string theory model of inflation (called DBI inflation) have a non-minimal kinetic term for the inflaton. These models generically predict a strong non-Gaussian signal, as well as possibly detectable gravitational waves. However the simplest implementation of this model into string theory is essentially ruled out by current experimental constraints. In this talk, I will discuss a new model using wrapped branes that can better match the Cosmic Microwave Background (CMB) data. In addition to its distinct signatures in the CMB, the end of inflation is a very stringy phenomena, and cosmic strings with a peculiar tension spectrum are produced.