We report a spin S = 3/2 triangular antiferromagnet with nearest-neighbor coupling J = 0.29 meV in La2Ca2MnO7. A genuinely two-dimensional, three-sublattice order develops below 2.80 K << the Weiss constant (25 K). The spin excitations deviate substantially from linear spin-wave theory, suggesting that magnon breakdown occurs in the material. Such a breakdown has been anticipated in recent theoretical studies, although the excitation spectrum remains to be accounted for.