We describe the beam position monitor system built for PEP-II, the B-factory at SLAG. The system reports beam position for bunches of between 5 x 10(8) and 8 x 10(10) electron charges, either singly or as continuous streams of bunches every 4.2 ns. Resolution at full charge is to be better than 10 microns in a single turn. Higher resolution is available via on-board multi-turn averaging. The position signal is processed in a 20 MHz bandwidth around 952 MHz. This bandwidth, rather broader than that typical of RF position monitors, allows good resolution for low charge single bunches. Additional novel features include stringent control of return losses in order to minimize cross-talk between nearby bunches which may contain very different charges. The digitizing electronics is multiplexed between the two PER-Il storage rings. Design, construction, and installation experience, as well as first results with beam are presented.