  Giant Radio Galaxies (GRGs) are the largest single structures in the
Universe. Exhibiting extended radio morphology, their projected sizes range
from 0.7 Mpc up to 4.9 Mpc. LOFAR has opened a new window on the discovery and
investigation of GRGs and, despite the hundreds that are today known, their
main growth catalyst is still debated. One natural explanation for the
exceptional size of GRGs is their old age. In this context, hard X-ray selected
GRGs show evidence of restarting activity, with the giant radio lobes being
mostly disconnected from the nuclear source, if any. In this paper, we present
the serendipitous discovery of a distant ($z=0.629$), medium X-ray selected GRG
in the Bo\"otes field. High-quality, deep Chandra and LOFAR data allow a robust
study of the connection between the nucleus and the lobes, at a larger redshift
so far inaccessible to coded-mask hard X-ray instruments. The radio morphology
of the GRG presented in this work does not show evidence for restarted
activity, and the nuclear radio core spectrum does not appear to be GPS-like.
On the other hand, the X-ray properties of the new GRG are perfectly consistent
with the ones previously studied with Swift/BAT and INTEGRAL at lower redshift.
In particular, the bolometric luminosity measured from the X-ray spectrum is a
factor of six larger than the one derived from the radio lobes, although the
large uncertainties make them formally consistent at $1\sigma$. Finally, the
moderately dense environment around the GRG, traced by the spatial distribution
of galaxies, supports recent findings that the growth of GRGs is not primarily
driven by underdense environments.
