The detection and measurement of gravitational-waves from coalescing neutron-star binary systems is an important science goal for ground-based gravitational-wave detectors. In addition to emitting gravitational-waves at frequencies that span the most sensitive bands of the LIGO and Virgo detectors, these sources are also amongst the most likely to produce an electromagnetic counterpart to the gravitational-wave emission. A joint detection of the gravitational-wave and electromagnetic signals would provide a powerful new probe for astronomy. Methods. During the period between September 19 and October 20, 2010, the first low-latency search for gravitational-waves from binary inspirals in LIGO and Virgo data was conducted. The resulting triggers were sent to electromagnetic observatories for followup. We describe the generation and processing of the low-latency gravitational-wave triggers. The results of the electromagnetic image analysis will be described elsewhere. Results. Over the course of the science run, three gravitational-wave triggers passed all of the low-latency selections. Of these, one was followed up by several of our observational partners. Analysis of the gravitational-wave data leads to an estimated false alarm rate of once every 6.4 days, falling far short of the requirement for a detection based solely on gravitational-wave data.