  We report on the discovery of ionised gas filaments in the circum-galactic
halo of the extremely metal-poor compact starburst SBS 0335-052E in a 1.5h
integration with the MUSE integral-field spectrograph. We detect these features
in H${\alpha}$ and [OIII] emission down to surface-brightness levels of $5
\times 10^{-19}$erg s$^{-1}$cm$^{-2}$arcsec$^{-2}$. The filaments have
projected diameters of 2.1 kpc and extend more than 9 kpc to the north and
north-west from the main stellar body. We also detect extended nebular HeII
$\lambda$4686 emission that brightens towards the north-west at the rim of a
star-burst driven super-shell, suggestive of a locally enhanced UV radiation
field due to shocks. We also present a velocity field of the ionised gas. The
filaments appear to connect seamlessly in velocity space to the kinematical
disturbances caused by the shell. Similar to high-$z$ star-forming galaxies,
the ionised gas in this galaxy is dispersion dominated. We argue that the
filaments were created via feedback from the starburst and that these ionised
structures in the halo may act as escape channels for Lyman continuum radiation
in this gas-rich system.
