We describe the implementation of a quantum random number generator (QRNG) on-board a nanosatellite deployed to low Earth orbit (LEO). The generator samples shot noise from an entangled photon-pair source based on spontaneous parametric down conversion, linking the entropy of the QRNG to fluctuations in the vacuum field. We present analysis of data acquired in lab-based acceptance testing as well as on-orbit, and use the source to implement a prototype for an off-grid randomness beacon.