We report the real-time discovery of a fast radio burst (FRB 131104) with the Parkes radio telescope in a targeted observation of the Carina dwarf spheroidal galaxy. The dispersion measure of the burst is 779 cm^-3 pc, exceeding predictions for the maximum line-of-sight Galactic contribution by a factor of 11. The temporal structure of the burst is characterized by an exponential scattering tail with a timescale of 2.0^+0.8_-0.5 ms at 1582 MHz that scales as frequency to the power

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... (all uncertainties represent 95 <0.64 ms due to dispersion smearing across a single spectrometer channel. Searches in 78 hours of follow-up observations with the Parkes telescope reveal no additional sporadic emission and no evidence for associated periodic radio emission. We hypothesize that the burst is associated with the Carina dwarf galaxy. Follow-up observations at other wavelengths are necessary to test this hypothesis.