Intermediate-resolution spectroscopy in the range 625-775 nm is reported for a faint very-late-type object discovered in two CCD images taken near the center of the Alpha Per cluster. The spectrum shows strong absorption molecular bands, H-alpha emission, and KI absorption typical of late-M dwarfs; H-alpha varies conspicuously. The effective temperature and luminosity derived from the spectrum and R,I band photometry are consistent with those expected for an Alpha Per (age of about 50 Myr) 0.07 solar mass substellar object. In this object the lithium resonance line at 670.8 nm should be detectable with higher resolution, higher SNR data, and this line is a potentially powerful spectroscopic discriminant between very low mass stars and brown dwarfs close to the substellar mass limit.