Molecular oxygen resembles 3d and 4f metals in exhibiting long-range spin ordering and strong electron correlation behaviors in compounds. Ferromagnetic spin ordering and half-metallicity, however, are quite elusive and have not been well acknowledged. In this Article, we address this issue by studying how spins will interact with each other if the oxygen dimers are arranged in a different way from that in the known superoxides and peroxides by first-principles calculations. Based on the results of a structure search, thermodynamic studies, and lattice dynamics, we show that tetragonal α-BaNaO₄ is a stable half-metal with a Curie temperature at 120 K, the first example in this class of compounds. Like 3d and 4f metals, the O₂ dimer carries a local magnetic moment of 0.5 μ_B due to the unpaired electrons in its π* orbitals. This compound can be regarded as forming from the O₂ dimer layers stacking in a head-to-head way. In contrast to the arrangement in AO₂ (A = K, Rb, Cs), the spins are ferromagnetically coupled both within and between the layers. Spin polarization occurs in π* orbitals, with spin-up electrons fully occupying the valence band and spin-down electrons partially occupying the conduction band, forming semiconducting and metallic channels, respectively. Our results highlight the importance of geometric arrangement of O₂ dimers in inducing ferromagnetism and other novel properties in O₂-dimer-containing compounds.