The Advanced Fiber Optic Echelle (AFOE) is a fiber-fed echelle spectrograph designed for the measurement of stellar Doppler shifts. Using a 2k x 2k CCD detector, it samples about 55% of the wavelength range between 450 nm and 700 nm (20 echelle orders) at a single shot, with spectral resolution R = 32000 to 70000 at 500 nm, depending on the slit width employed. The AFOE employs a number of devices to assure that the calibrations necessary for accurate Doppler measurements can be properly performed. The most important of these are: (1) coupling to the telescope via a double-scrambling optical fiber system; (2) continuous calibration of the wavelength scale and point-spread function by means of an atomic emission lamp entering the spectrograph via a separate fiber and/or a molecular iodine absorption cell; (3) availability of fiber-coupled sunlight for regular calibration against the solar spectrum; (4) appropriate mechanical design and active thermal control, yielding good mechanical stability. The AFOE is coupled to the Tillinghast 1.5-m telescope at the F. L. Whipple Observatory. It presently achieves S/N = 500 in the continuum near 500 nm in 60s when observing Arcturus (alpha-Boo, mV = -0.04). This noise level sets a limit of about 0.7 ms-1 to the Doppler precision attainable in this length of observing time. Currently, our actual frame-to-frame repeatability is worse than the photon noise limited value by about a factor of 3 for this bright star, and about 1.5 for stars with mV = 4. Work is continuing to refine data processing methods so that the ultimate noise limit may be approached more closely, and to improve the spectrograph's relatively low efficiency.