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Symmetry properties of the order parameter are among the most fundamental characteristics of a superconductor. UTe₂, which was found to feature an exceedingly large upper critical field and striking reentrant behavior at low temperatures, is widely believed to possess a spin-triplet pairing symmetry. However, unambiguous evidence for such a pairing symmetry is still lacking, especially at zero and low magnetic fields. The presence of an inversion crystalline symmetry in UTe₂requires that, if it is indeed a spin-triplet superconductor, the order parameter must be of odd parity. We report here phase-sensitive measurements of the symmetry of the orbital part of the order parameter using the Josephson effect. The selection rule in the orientation dependence of the Josephson coupling between In, ans-wave superconductor, and UTe₂suggests strongly that UTe₂possesses the odd-parity pairing state of B₁usymmetry near zero magnetic field, making it a spin-triplet superconductor. We also report the apparent formation of Andreev surface bound states on the (1−10) surface of UTe₂.