Emission signatures from galactic winds provide an opportunity to directly map the outflowing gas, but this is traditionally challenging because of the low surface brightness. Using very deep observations (27 h) of the Hubble Deep Field South with the Multi Unit Spectroscopic Explorer (MUSE) instrument, we identify signatures of an outflow in both emission and absorption from a spatially resolved galaxy at z = 1.29 with a stellar mass M⋆ = 8 × 109M⊙, star formation rate SFR = 77+40-25 M⊙ yr-1, and star formation rate surface brightness ΣSFR = 1.6M⊙ kpc-2 within the [Oii] λλ3727,3729 half-light radius R1/2, [OII] = 2.76 ± 0.17 kpc. From a component of the strong resonant Mg i