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We discovered novel nonunitary spin-triplet superconductivity in UTe₂, with the highest T_c and H_c2 among all candidates. Superconducting state closely resembles that of ferromagnetic superconductors, but the normal state is paramagnetic and shows no indication of magnetic ordering. UTe₂ exhibits an extremely large, anisotropic upper critical field Hc₂, temperature independent NMR Knight shift in the superconducting state, and a large residual normal electronic density of states indicating that half of the electrons remain ungapped. All these results strongly indicate that the superconductivity in UTe₂ is carried by nonunitary spin-triplet pairs. This discovery yields a new platform for encoding information using topological excitations and for manipulation of spin-polarized currents.