  We have obtained high-precision interferometric measurements of Vega with the
CHARA Array and FLUOR beam combiner in the K' band at projected baselines
between 103m and 273m. The measured visibility amplitudes beyond the first lobe
are significantly weaker than expected for a slowly rotating star characterized
by a single effective temperature and surface gravity. Our measurements, when
compared to synthetic visibilities and synthetic spectrophotometry from a
Roche-von Zeipel gravity-darkened model atmosphere, provide strong evidence for
the model of Vega as a rapidly rotating star viewed very nearly pole-on. Our
best fitting model indicates that Vega is rotating at ~91% of its angular
break-up rate with an equatorial velocity of 275 km/s. Together with the
measured vsin(i), this velocity yields an inclination for the rotation axis of
5 degrees. For this model the pole-to-equator effective temperature difference
is 2250 K, a value much larger than previously derived from spectral line
analyses. The derived equatorial T_eff of 7900 K indicates Vega's equatorial
atmosphere may be convective and provides a possible explanation for the
discrepancy. The model has a luminosity of ~37 Lsun, a value 35% lower than
Vega's apparent luminosity based on its bolometric flux and parallax, assuming
a slowly rotating star. The model luminosity is consistent with the mean
absolute magnitude of A0V stars. Our model predicts the spectral energy
distribution of Vega as viewed from its equatorial plane; a model which may be
employed in radiative models for the surrounding debris disk.
