Recent work has exploited pulsar survey data to identify temporally isolated, millisecond-duration radio bursts with large dispersion measures (DMs). These bursts have been interpreted as arising from a population of extragalactic sources, in which case they would provide unprecedented opportunities for probing the intergalactic medium; they may also be linked to new source classes. Until now, however, all so-called fast radio bursts (FRBs) have been detected with the Parkes radio telescope and its 13-beam receiver, casting some concern about the astrophysical nature of these signals. Here we present FRB 121102, the first FRB discovery from a geographic location other than Parkes. FRB 121102 was found in the Galactic anti-center region in the 1.4 GHz Pulsar Arecibo L-band Feed Array (ALFA) survey with the Arecibo Observatory with a DM = 557.4 ± 2.0 pc cm-3, pulse width of 3.0 ± 0.5 ms, and no evidence of interstellar scattering. The observed delay of the signal arrival time with frequency agrees precisely with the expectation of dispersion through an ionized medium. Despite its low Galactic latitude (b = -0.°2), the burst has three times the maximum Galactic DM expected along this particular line of sight, suggesting an extragalactic origin. A peculiar aspect of the signal is an inverted spectrum; we interpret this as a consequence of being detected in a sidelobe of the ALFA receiver. FRB 121102's brightness, duration, and the inferred event rate are all consistent with the properties of the previously detected Parkes bursts.