Nuclear magnetic resonance (NMR) measurements on the $^{195}$Pt nucleus in an aligned powder of the moderately heavy-fermion material U2PtC2 are consistent with spin-triplet pairing in its superconducting state. Across the superconducting transition temperature and to much lower temperatures, the NMR Knight shift is temperature independent for field both parallel and perpendicular to the tetragonal c-axis, expected for triplet equal-spin pairing superconductivity. The NMR spin-lattice relaxation rate 1/T$_1$, in the normal state, exhibits characteristics of ferromagnetic fluctuations, compatible with an enhanced Wilson ratio. In the superconducting state, 1/T$_1$ follows a power law with temperature without a coherence peak giving additional support that U$_2$PtC$_2$ is an unconventional superconductor. Bulk measurements of the AC-susceptibility and resistivity indicate that the upper critical field exceeds the Pauli limiting field for spin-singlet pairing and is near the orbital limiting field, an additional indication for spin-triplet pairing.
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