  Capturing planets in the act of losing their atmospheres provides rare
opportunities to probe their evolution history. Such analysis has been enabled
by observations of the helium triplet at 10833 \AA, but past studies have
focused on the narrow time window right around the planet's optical transit. We
monitored the hot Jupiter HAT-P-32 b using high-resolution spectroscopy from
the Hobby-Eberly Telescope covering the planet's full orbit. We detected helium
escaping HAT-P-32 b at a $14\sigma$ significance, with extended leading and
trailing tails spanning a projected length over 53 times the planet's radius.
These tails are among the largest known structures associated with an
exoplanet. We interpret our observations using three-dimensional hydrodynamic
simulations, which predict Roche Lobe overflow with extended tails along the
planet's orbital path.
