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We present Chandra X-ray imaging of a flux-limited sample of flat spectrum radio-emitting quasars with jet-like structure. X-rays are detected from 59% of 56 jets. No counter-jets were detected. The core spectra are fitted by power-law spectra with a photon index Γx, whose distribution is consistent with a normal distribution, with a mean of 1.61+0.04−0.05 and dispersion of 0.15+0.04−0.03. We show that the distribution of αrx, the spectral index between the X-ray and radio band jet fluxes, fits a Gaussian with a mean of 0.974 ± 0.012 and dispersion of 0.077 ± 0.008. We test the model in which kiloparsec-scale X-rays result from inverse Compton scattering of cosmic microwave background photons off the jet’s relativistic electrons (the IC-CMB model). In the IC-CMB model, a quantity Q computed from observed fluxes and the apparent size of the emission region depends on redshift as (1 + z)3+α. We fit Q ∝ (1 + z)a, finding a = 0.88 ± 0.90, and reject at 99.5% confidence the hypothesis that the average αrx depends on redshift in the manner expected in the IC-CMB model. This conclusion is mitigated by a lack of detailed knowledge of the emission region geometry, which requires deeper or higher resolution X-ray observations. Furthermore, if the IC-CMB model is valid for X-ray emission from kiloparsec-scale jets, then the jets must decelerate on average: bulk Lorentz factors should drop from about 15 to 2–3 between parsec and kiloparsec scales. Our results compound the problems that the IC-CMB model has in explaining the X-ray emission of kiloparsec-scale jets. [ABSTRACT FROM AUTHOR]