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

MUSE Illuminates Channels for Lyman Continuum Escape in the Halo of SBS 0335-52E