We have developed an approach to multiple-access lasercom that adopts the commercial paradigm of sharing the most expensive terminal resources among all users. Space-time division multiple access (STDMA), analogous to an optical space-time switch, hops the transmit beam and receive direction among multiple users and exchanges data while the beam dwells on a user. A key enabler of STDMA is electronic beam steering using liquid crystal optical phased arrays, which provides fast, precise, and agile beam re-pointing. We have built the first optical STDMA terminal, combining beam hopping between remote terminals with coherent combining of both transmit and receive apertures, which is an effective means for increasing antenna gain in systems for which large aperture components are impractical. Coherent beam combining provided the expected increase in antenna gain, and the terminal was found to re-point the beam among users quickly and precisely enough to suffer only minor throughput degradation. Communications test were performed using 10 Gb/s Ethernet for a single-aperture configuration. Performance is presented as a function of angle scan speed and STDMA dwell time per remote terminal. The results suggest that STDMA is a viable technology for supporting multiple-access space-based laser communication.