We report a remarkable Fe Kα fluorescence line profile in the Seyfert 1.9 galaxy MCG -5-23-16. The line is complex, consisting of a narrow core located at the galaxy's systemic velocity and wings to the red and blue sides of the core. This represents only the second detection with ASCA of an Fe Kα line profile with significant broadening blueward of 6.4 keV, consistent with Doppler boosting. The line core has an EW of ~60 eV and the wings have a combined EW of ~200 eV. The entire profile cannot be easily modeled with an emission line predicted from standard accretion disk theories. Instead, the line is marginally triple-peaked and is best described with three Gaussians having rest energies of 5.37+ 0.23−0.19 keV (FWHM = 30,200 km s-1), 6.37 ± 0.04 keV (FWHM < 6,600 km s-1), and 6.58+ 0.35−0.38 keV (FWHM = 75,300 km s-1). The line can also be modeled with a narrow Gaussian at ~6.4 keV and an emission line from an accretion disk viewed at an inclination angle of ~30° to 65°, depending on the ionization state of the gas. Within the context of the unified model, the most likely physical description of the complex profile is a superposition of an emission line from an accretion disk and a line that arises far from the disk in either the obscuring torus or the broad line region. This represents the first strong evidence for emission from two distinct X-ray reprocessors within a single Seyfert 1-type galaxy.