Unconventional superconductivity and, in particular, triplet superconductivity have been front and center of topological materials and quantum technology research. Here, we report our observation of triplet pairing in nonmagnetic CoSi2/TiSi2 heterostructures on silicon. CoSi2 undergoes a sharp superconducting transition at a critical temperature Tc ≃ 1.5 K, while TiSi2 is a normal metal. We investigate conductance spectra of both two-terminal CoSi2/TiSi2 contact junctions and three-terminal T-shaped CoSi2/TiSi2 superconducting proximity structures. Below Tc, we observe (i) a narrow zero-bias conductance peak on top of a broad hump, accompanied by two symmetric side dips in the contact junctions, (ii) a narrow zero-bias conductance peak in T-shaped structures, and (iii) hysteresis in the junction magnetoresistance. These three independent and complementary observations point to chiral p-wave pairing in CoSi2/TiSi2 heterostructures. The excellent fabrication compatibility of CoSi2 and TiSi2 with present-day silicon-based integrated-circuit technology suggests their potential use in scalable quantum-computing devices.