  PSR B1259-63 is a middle-aged radio pulsar (P=48 ms, tau=330 kyr,
Edot=8.3*10^{35} erg/s) in an eccentric binary (P_orb =3.4 yr, e=0.87) with a
high-mass Be companion, SS 2883. We observed the binary near apastron with the
Chandra ACIS detector on 2009 May 14 for 28 ks. In addition to the previously
studied pointlike source at the pulsar's position, we detected extended
emission on the south-southwest side of this source. The pointlike source
spectrum can be described by the absorbed power-law model with the hydrogen
column density N_H = (2.5+/-0.6)*10^{21} cm^{-2}, photon index Gamma =
1.6+/-0.1, and luminosity L_{0.5-8 keV} = 1.3*10^{33} d_3^2 erg/s, where d_3 is
the distance scaled to 3 kpc. This emission likely includes an unresolved part
of the pulsar wind nebula (PWN) created by the colliding winds from the pulsar
and the Be companion, and a contribution from the pulsar magnetosphere. The
extended emission apparently consists of two components. The highly significant
compact component looks like a southward extension of the pointlike source
image, seen up to about 4 arcsec from the pulsar position. Its spectrum has
about the same slope as the pointlike source spectrum, while its luminosity is
a factor of 10 lower. We also detected an elongated feature extended ~15 arcsec
southwest of the pulsar, but significance of this detection is marginal. We
tentatively interpret the resolved compact PWN component as a shocked pulsar
wind blown out of the binary by the wind of the Be component, while the
elongated component could be a pulsar jet.
