  We report on the formation and evolution of two large-scale,
synchrotron-emitting jets from the black hole candidate H 1743-322 following
its reactivation in 2003. In November 2003 after the end of its 2003 outburst,
we noticed, in observations with the Australia Telescope Compact Array, the
presence of a new and variable radio source about 4.6" to the East of H
1743-322, that was later found to move away from H 1743-322. In February 2004,
we detected a radio source to the West of H 1743-322, symmetrically placed
relative to the Eastern jet. In 2004, follow-up X-ray observations with {\em
Chandra} led to the discovery of X-ray emission associated with the two radio
sources. This likely indicates that we are witnessing the interaction of
relativistic jets from H 1743-322 with the interstellar medium causing in-situ
particle acceleration. The spectral energy distribution of the jets during the
decay phase is consistent with a classical synchrotron spectrum of a single
electron distribution from radio up to X-rays, implying the production of very
high energy ($>$ 10 TeV) particles in those jets. We discuss the jet
kinematics, highlighting the presence of a significantly relativistic flow in H
1743-322 almost a year after the ejection event.
