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Studies on oxide quasi-two-dimensional electron gas (q2DEG) have been a playground for the discovery of novel and sometimes unexpected phenomena, like the reported magnetism at the surface of SrTiO_{3} (001) and at the interface between nonmagnetic LaAlO_{3} and SrTiO_{3} band insulators. However, magnetism in this system is weak and there is evidence of a nonintrinsic origin. Here, by using in situ high-resolution angle-resolved photoemission, we demonstrate that ferromagnetic EuTiO_{3}, the magnetic counterpart of SrTiO_{3} in the bulk, hosts a q2DEG at its (001) surface. This is confirmed by density functional theory calculations with Hubbard U terms in the presence of oxygen divacancies in various configurations, all of them leading to a spin-polarized q2DEG related to the ferromagnetic order of Eu-4f magnetic moments. The results suggest EuTiO_{3}(001) as a new material platform for oxide q2DEGs, characterized by broken inversion and time-reversal symmetries.