Capturing planets in the act of losing their atmospheres provides rare opportunities to probe their evolution history. This analysis has been enabled by observations of the helium triplet at 10,833 angstrom, 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 14σ 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.