  We report the discovery of a double-peaked Lyman-alpha profile in a galaxy at
$z=6.803$, A370p\_z1, in the parallel Frontier Field of Abell 370. The velocity
separation between the blue and red peaks of the Lyman-$\alpha$ profile
($\Delta v=101_{-19}^{+38} (\pm48)\,\text{km s}^{-1}$) suggests an extremely
high escape fraction of ionising photons $> 59(51)\% (2\sigma)$. The spectral
energy distribution indicates a young ($50$ Myr), star-forming ($12\pm 6 \,
\rm{M}_\odot \rm{yr}^{-1}$) galaxy with an IRAC excess implying strong
[OIII]+H$\beta$ emission. On the basis of the high escape fraction measured, we
demonstrate that A370p\_z1 was solely capable of creating an ionised bubble
sufficiently large to account for the blue component of its Lyman-alpha
profile. We discuss whether A370p\_z1 may be representative of a larger
population of luminous $z\simeq7$ double-peaked Lyman-alpha emitting sources
with high escape fractions that self-ionised their surroundings without
contributions from associated UV-fainter sources.
