PSR J0108-1431 is a nearby, 170 Myr old, very faint radio pulsar near the pulsar death line in the P-Pdot diagram. We observed the pulsar field with the Chandra X-ray Observatory and detected a point source (53 counts in a 30 ks exposure, energy flux (9+/-2)times 10^{-15} ergs cm^{-2} s^{-1} in the 0.3-8 keV band) close to the radio pulsar position. Based on the large X-ray/optical flux ratio at the X-ray source position, we conclude that the source is the X-ray counterpart of PSR J0108-1431.The pulsar spectrum can be described by a power-law model with photon index Gamma approx 2.2 and luminosity L_{0.3-8 keV} sim 2times 10^{28} d_{130}^2 ergs s^{-1}, or by a blackbody model with the temperature kTapprox 0.28 keV and bolometric luminosity L_{bol} sim 1.3times 10^{28} d_{130}^2 ergs s^{-1}, for a plausible hydrogen column density NH = 7.3times 10^{19} cm^{-2} (d_{130}=d/130 pc). The pulsar converts sim 0.4% of its spin-down power into the X-ray luminosity, i.e., its X-ray efficiency is higher than for most younger pulsars. From the comparison of the X-ray position with the previously measured radio positions, we estimated the pulsar proper motion of 0.2 arcsec yr^{-1} (V_perp sim 130 d_{130} km s^{-1}), in the south-southeast direction.
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