Context. Extragalactic Fast X-ray Transients (FXRTs) are short flashes of X-ray photons spanning a few seconds to hours, with an uncertain origin. Aims. Our ignorance about their physical mechanisms and progenitor systems is due in part to the lack of clear multi-wavelength counterparts in most cases,because they only have been identified serendipitously. Methods. We develop a systematic search of FXRTs using a straightforward X-ray flare search algorithm, in the Chandra Source Catalog (Data Release 2.0; 169.6 Ms over 592.4 deg 2 using only observations with |b|>10 • and before 2015), incorporating various multi-wavelength constraints to rule out Galactic contamination and characterize the candidates. Results. We report the detection of 14 FXRT candidates from a parent sample of 214,701 sources. Candidates have peak 0.5-7 keV fluxes between 1×10 −13 to 2×10 −10 erg cm −2 s −1 and T 90 values from 4 to 48 ks. The sample can be subdivided into two groups: six "nearby" FXRTs that occurred within d 100 Mpc and eight "distant" FXRTs with likely redshifts 0.1. Three distant FXRT candidates exhibit light curves with a plateau (≈1-3 ks duration) followed by a power-law decay and X-ray spectral softening, similar to what was observed for the previously reported FXRT CDF-S XT2, a proposed magnetar-powered binary neutron star merger event. After applying completeness corrections, we calculate event rates for the nearby and distant samples of 53.7 +22.6 −15.1 and 28.2 +9.8 −6.9 deg −2 yr −1 , respectively. Conclusions. This novel sample of Chandra-detected extragalactic FXRT candidates, although modest in size, breaks new ground in terms of characterizing the diverse properties, nature, and possible progenitors of these enigmatic events.