We have identified twenty-seven candidate very low mass members of the relatively young Alpha Persei open cluster from a six square degree CCD imaging survey . Based on their I magnitudes and the nominal age and distance to the cluster , these objects should have masses less than 0.1 \cal { M } _ { \mathord { \odot } } if they are cluster members . We have subsequently obtained intermediate resolution spectra of seventeen of these objects using the Keck II telescope and LRIS spectrograph . We have also obtained near-IR photometry for many of the stars . Our primary goal was to determine the location of the “ lithium depletion boundary ” and hence to derive a precise age for the cluster . Most of our program objects have radial velocities consistent with cluster membership , moderately strong H \alpha emission , and spectral types M5.5 to M8 as expected from their ( R-I ) _ { C } colors . We detect lithium with equivalent widths greater than or equal to 0.4 Å in five of the program objects . We have constructed a color-magnitude diagram for the faint end of the Alpha Persei main sequence , including stars for which high S/N spectra in the region of the lithium \lambda 6708Å absorption line have been obtained . These data allow us to accurately determine the Alpha Persei single-star lithium depletion boundary at M ( I _ { C } ) = 11.47 , M ( Bol ) = 11.42 , ( R-I ) _ { C 0 } = 2.12 , spectral type M6.0 . By reference to theoretical evolutionary models , this converts fairly directly into an age for the Alpha Persei cluster of 90 \pm 10 Myr . That age is considerably older than most previously quoted ages for the cluster , but consistent with ages estimated from the upper-main sequence turnoff using recent models which include a moderate amount of convective core overshoot . At this age , the two faintest of our spectroscopically confirmed members should be sub-stellar ( i.e. , brown dwarfs ) according to theoretical models .