  Jets from rotation-powered pulsars have so far only been observed in systems
moving subsonically trough their ambient medium and/or embedded in their
progenitor supernova remnant (SNR). Supersonic runaway pulsars are also
expected to produce jets, but they have not been confirmed so far. We
investigated the nature of the jet-like structure associated to the INTEGRAL
source IGR J11014-6103 (the "Lighthouse nebula"). The source is a neutron star
escaping its parent SNR MSH 11-61A supersonically at a velocity exceeding 1000
km/s. We observed the Lighthouse nebula and its jet-like X-ray structure
through dedicated high spatial resolution observations in X-rays (Chandra) and
radio band (ATCA). Our results show that the feature is a true pulsar's jet. It
extends highly collimated over >11pc, displays a clear precession-like
modulation, and propagates nearly perpendicular to the system direction of
motion, implying that the neutron star's spin axis in IGR J11014-6103 is almost
perpendicular to the direction of the kick received during the supernova
explosion. Our findings suggest that jets are common to rotation-powered
pulsars, and demonstrate that supernovae can impart high kick velocities to
misaligned spinning neutron stars, possibly through distinct, exotic,
core-collapse mechanisms.
