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The low-temperature specific heat of single-crystal samples of superconducting MgCNi_3 with typical dimensions 200 μm were measured for the first time. A computer controlled ac microcalorimeter using an optical fiber and an infrared light-emitting diode as the heat source was used down to 2 K at magnetic fields up to 8 T. The specific heat data suggest a moderate coupling in MgCNi_3.