We have conducted a systematic study of X-ray emission from ultra-compact dwarf ( UCD ) galaxies and extended star clusters ( ESCs ) , based on archival Chandra observations . Among a sample of 511 UCDs and ESCs complied from the literature , 17 X-ray counterparts with 0.5-8 keV luminosities above \sim 5 \times 10 ^ { 36 } { ~ { } erg~ { } s ^ { -1 } } are identified , which are distributed in eight early-type host galaxies . To facilitate comparison , we also identify X-ray counterparts of 360 globular clusters ( GCs ) distributed in four of the eight galaxies . The X-ray properties of the UCDs and ESCs are found to be broadly similar to those of the GCs . The incidence rate of X-ray-detected UCDs and ESCs , ( 3.3 \pm 0.8 ) % , while lower than that of the X-ray-detected GCs [ ( 7.0 \pm 0.4 ) % ] , is substantially higher than expected from the field populations of external galaxies . A stacking analysis of the individually undetected UCDs/ESCs further reveals significant X-ray signals , which corresponds to an equivalent 0.5-8 keV luminosity of \sim 4 \times 10 ^ { 35 } { ~ { } erg~ { } s ^ { -1 } } per source . Taken together , these provide strong evidence that the X-ray emission from UCDs and ESCs is dominated by low-mass X-ray binaries having formed from stellar dynamical interactions , consistent with the stellar populations in these dense systems being predominantly old . For the most massive UCDs , there remains the possibility that a putative central massive black hole gives rise to the observed X-ray emission .