We present 35 ks Chandra ACIS observations of the 42 Myr old radio pulsar PSR B1451-68. A point source is detected 0.32 +/- 0.73 from the expected radio pulsar position. It has ~200 counts in the 0.3-8 keV energy range. We identify this point source as the X-ray counterpart of the radio pulsar. PSR B1451-68 is located close to a 2MASS point source, for which we derive 7% as the upper limit on the flux contribution to the measured pulsar X-ray flux. The pulsar spectrum can be described by either a power-law model with photon index Gamma=2.4 (+0.4/-0.3) and a unrealistically high absorbing column density N(H)= (2.5 (+1.2/-1.3)) * 10^(21) cm^-2, or by a combination of a kT=0.35 (+0.12/-0.07) keV blackbody and a Gamma = 1.4 +/- 0.5 power-law component for N(H)[DM]= 2.6 * 10^(20) cm^-2, estimated from the pulsar dispersion measure. At the parallactic, Lutz-Kelker bias corrected distance of 480 pc, the non-thermal X-ray luminosities in the 0.3-8 keV energy band are either Lx(nonth)= (11.3 +/- 1.7) * 10^(29) erg/s or Lx(nonth)= (5.9 (+4.9/-5.0)) * 10^(29) erg/s, respectively. This corresponds to non-thermal X-ray efficiencies of either eta(nonth)= Lx(nonth) / (dE/dt) ~ 0.005 or 0.003, respectively.
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