We report the discovery of bulk superconductivity in the ternary intermetallics YNiSi 3 and LuNiSi 3. High-quality single crystals were grown via the Sn-flux method and studied using magnetization, specific-heat, and resistivity measurements at low temperatures. The critical temperatures obtained from these different techniques are in very good agreement and yield T c = 1.36(3) K and T c = 1.61(2) K for YNiSi 3 and LuNiSi 3 , respectively. Magnetization measurements indicate that both compounds are among the rare cases where type-I superconductivity occurs in a ternary intermetallic, however, the jump in the specific heat at the transition is lower than the value expected from BCS theory (C el /γ n T c = 1.43) in both materials and is equal to 1.14(9) and 0.71(5) for the Y and Lu compounds, respectively. Resistivity measurements exhibit sharp transitions but with critical fields μ 0 H c (0) (≈0.05 T for YNiSi 3 and ≈0.08 T for LuNiSi 3) considerably higher than those obtained from the magnetization and specific heat (≈0.01 T). First-principles density functional theory calculated electronic structure shows that these compounds have highly anisotropic and complex Fermi surfaces with one electronic and two holelike branches. One hole branch and the electron branch have a large cylindrical topology connecting the first Brillouin-zone boundaries, the former being built up by the hybridization of Y(Lu) d, Ni d, and Si p states, and the latter being built up by Ni d and Si p states. The calculated phononic structures indicate that the coupling of the Y(Lu), Ni d, and Si p electrons in the low-lying optical phonon branches is responsible for the formation of Cooper pairs and the observed superconducting state. Therefore, these compounds can be classified as anisotropic three-dimensional metals with multiband superconducting ground states in the weak-coupling regime.