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,

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... mmetrically placed relative to the Eastern jet. In 2004, follow-up X-ray observations with 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.