Double-peaked Lyman-$\alpha$ emission at z=6.803: a reionisation-era galaxy self-ionising its local HII bubble

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.