Electrical-resistivity, magnetic-susceptibility and specific-heat data reveal that the bulk phase transition at 2.63 similar to 2.86 K (10 similar to 90% values) in LaNiC2 is to a superconducting ground state. The normal-state specific-heat data can be fitted to the expression C-n = gamma T + beta T-3 (3 K < T < 7 K) by a least-squares analysis, where gamma = 7.83 mJ/mol K-2 and beta = 0.0635 mJ/mol K-4, resulting in a Debye temperature theta(D) = 496 K. A special emphasis is on the specific heal in the superconducting state below 1.6 K; C-s is not exponential but has a power-law form: C-s approximate to 3.5(gamma T-c)(T/T-c)(3). According to the observed specific-heat data, we suggest that LaNiC2 belongs to a nonconventional BCS superconductor. In addition, LaNiC2 is the first nickel-based ternary-carbide superconductor.