We present a simple mechanism for obtaining large-field inflation, and hence a gravitational wave signature, from string theory compactified on twisted tori. For nil manifolds, we obtain a leading inflationary potential proportional to in terms of the canonically normalized field , yielding predictions for the tilt of the power spectrum and the tensor-to-scalar ratio, and with 60 e-foldings of inflation; we note also the possibility of a variant with a candidate inflaton potential proportional to . The basic mechanism involved in extending the field range—monodromy in -branes as they move in circles on the manifold—arises in a more general class of compactifications, though our methods for controlling the corrections to the slow-roll parameters require additional symmetries.