We report the successful fitting of a Roche model, with a surface temperature gradient following the von Zeipel gravity darkening law, to observations of Altair made with the Navy Prototype Optical Interferometer. We confirm the claim by Ohishi et al. that Altair displays an asymmetric intensity distribution due to rotation, the first such detection in an isolated star. Instrumental effects due to the high visible flux of this first magnitude star appear to be the limiting factor in the accuracy of this fit, which nevertheless indicates that Altair is rotating at 0.90+/-0.02 of its breakup (angular) velocity. Our results are consistent with the apparent oblateness found by van Belle et al. and show that the true oblateness is significantly larger owing to an inclination of the rotational axis of ~64° to the line of sight. Of particular interest, we conclude that instead of being substantially evolved as indicated by its classification, A7 IV-V, Altair is only barely off the zero-age main sequence and represents a good example of the difficulties rotation can introduce in the interpretation of this part of the HR diagram.