We present a simple mechanism for obtaining large-field inflation, and hence a gravitational wave signature, from string theory. They basic structure involved in extending the field range -- monodromies in the presence of wrapped D-branes combined with symmetries protecting the flatness of an inflaton potential -- arises in several classes of string compactifications. In one example, type IIA string theory on Nil manifolds with a space-time filling D4-brane moving along an internal circle, we obtain a leading inflationary potential proportional to phi^(2/3) in terms of the canonically normalized field phi, yielding predictions for the tilt of the power spectrum and the tensor-to-scalar ratio, n_s = 0.98 and r = 0.04 with 60 e-foldings of inflation. In a second example, wrapped branes can also introduce a monodromy that extends the field range of individual closed-string axions to beyond the Planck scale. Shift symmetries of the system naturally control corrections to the axion potential. This suggests a general mechanism for chaotic inflation driven by monodromy-extended closed-string axions. We systematically analyze this possibility and show its compatibility with moduli stabilization in e.g. warped Calabi-Yau manifolds. In this broad class of models, the potential is linear in the canonical inflaton field, predicting a tensor to scalar ratio r = 0.07 accessible to upcoming cosmic microwave background (CMB) observations.