Recent works have discovered two fast ($approx 10$ ks) extragalactic X-ray transients in the Chandra Deep Field-South (CDF-S XT1 and XT2). These findings suggest that a large population of similar extragalactic transients might exist in archival X-ray observations. We develop a method that can effectively detect such transients in a single Chandra exposure, and systematically apply it to Chandra surveys of CDF-S, CDF-N, DEEP2, UDS, COSMOS, and E-CDF-S, totaling 19~Ms of exposure. We find 13 transient candidates, including CDF-S XT1 and XT2. With the aid of available excellent multiwavelength observations, we identify the physical nature of all these candidates. Aside from CDF-S XT1 and XT2, the other 11 sources are all stellar objects, and all of them have $z$-band magnitudes brighter than 20. We estimate an event rate of $59^{+77}_{-38} rm{evt yr^{-1} deg^{-2}}$ for CDF-S XT-like transients with 0.5-7 keV peak fluxes $log F_{rm peak} gtrsim -12.6$ (erg cm$^{-2}$ s$^{-1}$). This event rate translates to $approx 15^{+20}_{-10}$ transients existing among Chandra archival observations at Galactic latitudes $|b|>20^{circ}$, which can be probed in future work. Future missions such as Athena and the Einstein Probe with large grasps (effective area $times$ field of view) are needed to discover a large sample ($sim$ thousands) of fast extragalactic X-ray transients.
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