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 ($\Delta v=101_{-19}^{+38} (\pm 48), \rm{km s}^{-1}$) 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.