  Atmospheric escape shapes the fate of exoplanets, with statistical evidence
for transformative mass loss imprinted across the mass-radius-insolation
distribution. Here we present transit spectroscopy of the highly irradiated,
low-gravity, inflated hot Saturn HAT-P-67 b. The Habitable Zone Planet Finder
(HPF) spectra show a detection of up to 10% absorption depth of the 10833
Angstrom Helium triplet. The 13.8 hours of on-sky integration time over 39
nights sample the entire planet orbit, uncovering excess Helium absorption
preceding the transit by up to 130 planetary radii in a large leading tail.
This configuration can be understood as the escaping material overflowing its
small Roche lobe and advecting most of the gas into the stellar -- and not
planetary -- rest frame, consistent with the Doppler velocity structure seen in
the Helium line profiles. The prominent leading tail serves as direct evidence
for dayside mass loss with a strong day-/night- side asymmetry. We see some
transit-to-transit variability in the line profile, consistent with the
interplay of stellar and planetary winds. We employ 1D Parker wind models to
estimate the mass loss rate, finding values on the order of $2\times10^{13}$
g/s, with large uncertainties owing to the unknown XUV flux of the F host star.
The large mass loss in HAT-P-67 b represents a valuable example of an inflated
hot Saturn, a class of planets recently identified to be rare as their
atmospheres are predicted to evaporate quickly. We contrast two physical
mechanisms for runaway evaporation: Ohmic dissipation and XUV irradiation,
slightly favoring the latter.
