We report on spectral and intensity variability analysis from a Chandra /ACIS-S observation of the transient , type-I X-ray bursting low-mass X-ray binary Cen X-4 . The quiescent X-ray spectrum during this observation is statistically identical to one observed previously with BeppoSAX , and close , but not identical , to one observed previously with ASCA . The X-ray spectrum is best described as a pure Hydrogen atmosphere thermal spectrum plus a power-law component that dominates the spectrum above 2 keV . The best-fit radius of the neutron star is r = 12.9 \pm 2.6 ( d / 1.2 { kpc } ) km if the interstellar absorption is fixed at the value implied by the optical reddening . Allowing the interstellar absorption to be a free parameter yields r = 19 ^ { +45 } _ { -10 } ( d / 1.2 { kpc } ) km ( 90 % confidence ) . The thermal spectrum from the neutron star surface is inconsistent with a solar metallicity . We find a 3 \sigma upper-limit of root-mean-square variability \leq 18 \% ( 0.2-2.0 keV ; 0.0001-1 Hz ) during the observation . On the other hand , the 0.5-10.0 keV luminosity decreased by 40 \pm 8 % in the 4.9 years between the ASCA and Chandra observations . This variability can be attributed to the power-law component . Moreover , we limit the variation in thermal temperature to \lesssim 10 % over these 4.9 years . The stability of the thermal temperature and emission area radius supports the interpretation that the quiescent thermal emission is due to the hot neutron star core .