With powder-x-ray-diffraction methods, the ternary compound LaNiSi has been identified to have a LaPtSi-type crystal structure with four formula units in a unit cell of the space group I4(1)md with dimensions a = 4.181(1) angstrom, c = 14.069(8) angstrom. The agreement of the transition temperature T(c) = 1.20 approximately 1.26 K (10 approximately 90 % values) measured by ac-susceptibility and heat-capacity techniques provides clear evidence of bulk superconductivity in LaNiSi. The normal-state specific-heat data can be fit to the expression C(n) = gammaT + betaT3 by a least-squares analysis, where gamma = 8.89 mJ/mol K2 and beta = 0.487 mJ/mol K4, resulting in a Debye temperature THETA(D) = 229 K. Below T(c), the specific-heat data have a dominant low-temperature behavior of the form exp[-DELTA(0)/k(B)T], where the order parameter 2DELTA(0) = 3.5k(B)T(c). In addition, the measured heat-capacity jump DELTAC at the transition point is found to be equal to 1.46 gammaT(c), implying that LaNiSi is a weakly coupled superconductor.