To monitor small earthquakes on the ocean bottom or in remote areas on land, a seismic recording system should operate at low power for extended periods of time, should reproduce three components of ground motion with a large dynamic range, and should preferably be small and inexpensive. We describe such a system based on an event detector, which continuously surveys the background noise, sets a threshold, and triggers an inexpensive digital tape recorder when a seismic signal exceeds that threshold. Event recording offers the advantages over conventional continuous recording of more efficient use of storage capacity and easier later interpretation. A key element of the system is a continuously updated semiconductor buffer memory, which assures that first arrivals are included. Average power consumption is about a watt. The system design is easily adaptable to monitoring other types of rare events of unpredictable occurrence.