We present a detailed analysis of the orbit of Charon where we show its orbit to be circular. This analysis explores the effects of surface albedo variations on the astrometry and the resulting errors in the orbital elements. We present two new epochs of data from the Hubble Space Telescope taken in 2008 and 2010 and combine that with a re-analysis of previously published data from 1992 and 2002. Our adopted two-body Keplerian orbital elements for Charon are P = 6.3872273 ± 0.0000003 days, a = 19573 ± 2 km, e = 0., i = 96.218 ± 0.008 deg, L = 4.50177 ± 0.00018 rad, and Ω = 3.89249 ± 0.00012 rad for an epoch of JDT = 2452600.5 in the J2000 reference frame. The 1σ upper limit to the eccentricity is 7.5 × 10-5. The predicted uncertainty in the position of Charon relative to Pluto at the time of the New Horizons encounter based on this orbit is 8 km.