We present multiple epochs of H \alpha spectroscopy for 47 members of the open cluster NGC 3766 to investigate the long term variability of its Be stars . Sixteen of the stars in this sample are Be stars , including one new discovery . Of these , we observe an unprecedented 11 Be stars that undergo disk appearances and/or near disappearances in our H \alpha spectra , making this the most variable population of Be stars known to date . NGC 3766 is therefore an excellent location to study the formation mechanism of Be star disks . From blue optical spectra of 38 cluster members and existing Strömgren photometry of the cluster , we also measure rotational velocities , effective temperatures , and polar surface gravities to investigate the physical and evolutionary factors that may contribute to the Be phenomenon . Our analysis also provides improvements to the reddening and distance of NGC 3766 , and we find E ( B - V ) = 0.22 \pm 0.03 and ( V - M _ { V } ) _ { 0 } = 11.6 \pm 0.2 , respectively . The Be stars are not associated with a particular stage of main-sequence evolution , but they are a population of rapidly rotating stars with a velocity distribution generally consistent with rotation at 70 - 80 % of the critical velocity , although systematic effects probably underestimate the true rotational velocities so that the rotation is much closer to critical . Our measurements of the changing disk sizes are consistent with the idea that transitory , nonradial pulsations contribute to the formation of these highly variable disks .