Context. Extragalactic fast X-ray transients (FXRTs) are short flashes of X-ray photons of unknown origin that last a few seconds to hours. Aims. Our ignorance about their physical mechanisms and progenitor systems is due in part to the lack of clear multiwavelength counterparts in most cases, because FXRTs have only been identified serendipitously. Methods. We develop a systematic search for FXRTs in the Chandra Source Catalog (Data Release 2.0; 169.6 Ms over 592.4 deg², using only observations with |b|> 10° and before 2015), using a straightforward X-ray flare search algorithm and incorporating various multiwavelength 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 and 2 × 10⁻¹⁰ erg cm⁻² s⁻¹ and T₉₀ 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_−15.1^+22.6 and 28.2_−6.9^+9.8 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.