A small fraction of the telluric standards observed as part of the SDSS-III APOGEE survey have been discovered to be B-type emission line stars, many of which are likely to be classical Be stars. The H I Brackett line profiles of these systems are being characterized to study the properties of the circumstellar disks associated with these objects (see e.g. Chojnowski et al 2012). We present the analysis of a particularly unusual one of these blue emission line stars, which exhibits double-peaked H I Brackett lines that extend to abnormally large velocities (FWHM ~1380 km/s) for typical classical Be stars. Analysis of follow-up 0.35 - 2.46 micron spectroscopy and the system's spectral energy distribution also reveals puzzling deviations from the behavior of typical classical Be stars. We discuss the range of possible evolutionary scenarios for this emission-line star.