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In this paper we obtain a model of Natural Inflation from string theory witha Planckian decay constant. We investigate D-brane dynamics in the backgroundof the warped resolved conifold (WRC) throat approximation of Type IIB stringcompactifications on Calabi-Yau manifolds. When we glue the throat to a compactbulk Calabi-Yau, we generate a D-brane potential which is a solution to theLaplace equation on the resolved conifold. We can exactly solve this equation,including dependence on the angular coordinates. The solutions are valid downto the tip of the resolved conifold, which is not the case for the morecommonly used deformed conifold. This allows us to exploit the effect of thewarping, which is strongest at the tip. We inflate near the tip using anangular coordinate of a D5-brane in the WRC which has a discrete shiftsymmetry, and feels a cosine potential, giving us a model of Natural Inflation,from which it is possible to get a Planckian decay constant whilst maintainingcontrol over the backreaction. This is because the decay constant for a wrappedbrane contains powers of the warp factor, and so can be made large, while thewrapping parameter can be kept small enough so that backreaction is undercontrol.

D-brane Potentials in the Warped Resolved Conifold and Natural Inflation