We report results of the first search specifically targeting short-timescale X-ray flares from low-mass X-ray binaries in an early-type galaxy . A new method for flare detection is presented . In NGC 4697 , the nearest , optically luminous , X-ray faint elliptical galaxy , 3 out of 157 sources are found to display flares at > 99.95 \% probability , and all show more than one flare . Two sources are coincident with globular clusters and show flare durations and luminosities similar to ( but larger than ) Type-I X-ray superbursts found in Galactic neutron star ( NS ) X-ray binaries ( XRBs ) . The third source shows more extreme flares . Its flare luminosity ( \sim 6 \times 10 ^ { 39 } erg s ^ { -1 } ) is very super-Eddington for an NS and is similar to the peak luminosities of the brightest Galactic black hole ( BH ) XRBs . However , the flare duration ( \sim 70 s ) is much shorter than are typically seen for outbursts reaching those luminosities in Galactic BH sources . Alternative models for the flares are considered .