  We report the first X-ray detection of the radio pulsar PSR B1757-24 using
the Chandra X-ray Observatory. The image reveals point-source emission at the
pulsar position, consistent with being magnetospheric emission from the pulsar.
In addition, we detect a faint tail extending nearly 20" east of the pulsar, in
the same direction and with comparable morphology to the pulsar's well-studied
radio tail. The X-ray tail is unlikely to be emission left behind following the
passage of the pulsar, but rather is probably from synchrotron-emitting pulsar
wind particles having flow velocity ~7000 km/s. Assuming the point-source X-ray
emission is magnetospheric, the observed X-ray tail represents only ~0.01% of
the pulsar's spin-down luminosity, significantly lower than the analogous
efficiencies of most known X-ray nebulae surrounding rotation-powered pulsars.
