BOSS-EUVLG1 is the most ultraviolet (UV) and Ly alpha luminous galaxy to be going through a very active starburst phase detected thus far in the Universe. It is forming stars at a rate of 955 +/- 118 M-circle dot yr(-1). We report the detection of a broad H alpha component carrying 25% of the total H alpha flux. The broad H alpha line traces a fast and massive ionized gas outflow characterized by a total mass, log(M-out[M-circle dot]), of 7.94 +/- 0.15, along with an outflowing velocity (V-out) of 573 +/- 151 km s(-1) and an outflowing mass rate (M-out) of 44 +/- 20 M-circle dot yr(-1). The presence of the outflow in BOSS-EUVLG1 is also supported by the identification of blueshifted UV absorption lines in low and high ionization states. The energy involved in the H alpha outflow can be explained by the ongoing star formation, without the need for an active galactic nucleus to be included in the scenario. The derived low mass-loading factor (eta =0.05 +/- 0.03) indicates that, although it is massive, this phase of the outflow cannot be relevant for the quenching of the star formation, namely, the negative feedback. In addition, only a small fraction (