  We present a Chandra Director's Discretionary Time observation of PSR
J1119-6127 and its compact X-ray pulsar wind nebula (PWN) obtained on 27
October 2016, three months after the Fermi and Swift detection of millisecond
bursts in hard X-rays, accompanied by >160 times increase in flux. This
magnetar-like activity, the first observed from a rotation-powered radio
pulsar, provides an important probe of the physical processes that
differentiate radio pulsars from magnetars. The post-burst X-ray spectrum of
the pulsar can be described by a single powerlaw model with a photon index of
2.0\pm0.2 and an unabsorbed flux of 5.7e-12 ergs/cm^2/s in the 0.5-7.0 keV
energy range. At the time of Chandra observations, the pulsar was still
brighter by a factor of ~22 in comparison with its quiescence. The X-ray images
reveal a nebula brighter than in the pre-burst Chandra observations (from 2002
and 2004), with an unabsorbed flux of 2.2e-13 ergs/cm^-2/s. This implies a
current X-ray efficiency of ~0.001 at a distance of 8.4 kpc. In addition, a
faint torus-like structure is visible along the southeast-northwest direction
and a jet-like feature perpendicular to the torus towards the southwest. The
PWN is best fitted by an absorbed powerlaw with a photon index of 2.2\pm0.5
(post-burst). While the pulsar can still be energetically powered by rotation,
the observed changes in PSR~J1119-6127 and its PWN following the magnetar-like
bursts point to an additional source of energy powered by its high-magnetic
field.
