  We present the first X-ray detection of the very young pulsar PSR J1357-6429
(characteristic age of 7.3 kyr) using data from the XMM-Newton and Chandra
satellites. We find that the spectrum is well described by a power-law plus
blackbody model, with photon index Gamma=1.4 and blackbody temperature kT=160
eV. For the estimated distance of 2.5 kpc, this corresponds to a 2-10 keV
luminosity of about 1.2E+32 erg/s, thus the fraction of the spin-down energy
channeled by PSR J1357-6429 into X-ray emission is one of the lowest observed.
The Chandra data confirm the positional coincidence with the radio pulsar and
allow to set an upper limit of 3E+31 erg/s on the 2-10 keV luminosity of a
compact pulsar wind nebula. We do not detect any pulsed emission from the
source and determine an upper limit of 30% for the modulation amplitude of the
X-ray emission at the radio frequency of the pulsar.
