We present infrared interferometric angular size measurements for the A7IV-V star Altair which indicate a non-circular projected disk brightness distribution. Given the known rapid rotation of this star, we model the data as arising from an elongated rigid atmosphere. To first order, an ellipse may be fit to our interferometric diameter measurements, with major and minor axes of 2a=3.461+-0.038 milliarcseconds (mas) and 2b=3.037+-0.069 mas, respectively, for a difference of 424+-79 microarcseconds between 2a and 2b, and with an axial ratio of a/b =1.140+-0.029. Assuming that the apparent oblateness of the photosphere is due to the star's rapid rotation, a more rigorous evaluation of the observation data in the context of a rigidly rotating Roche model shows that an estimate of v sin i = 210+-13 km/s can be derived that is independent of spectroscopic techniques. Also derived are values for the mean effective temperature, the mean linear radius, and an observational constraint upon the the relationship between rotation velocity and stellar inclination is established. Altair is the first main sequence star for which direct observations of an oblate photosphere have been reported, and the first star forwhich v sin i has been established from observations of the star's photospheric geometry.