Chiral crystals provide a unique setting where broken inversion symmetry, strong spin-orbit coupling, and electronic topology intertwine, yet superconductivity in intrinsically chiral materials remains rare. Here, we report unconventional superconductivity in the chiral topological semimetal Ag₂Pd₃S, an enantiomorphic analog of natural mineral coldwellite, crystallizing in the right-handed space group P4₁32. Bulk superconductivity with a transition temperature T_C = 1.1(2) K is confirmed by electrical resistivity, magnetization, and specific-heat measurements. Muon spin rotation and relaxation (μSR) experiments reveal a fully gapped superconducting state that spontaneously time-reversal symmetry (TRS) breaking establishing Ag₂Pd₃S as the first chiral topological semimetal superconductor exhibiting intrinsic TRS breaking. First-principles calculations uncover multiple multifold band crossings near the Fermi level, hosting Kramers-Weyl, double spin-1, and spin-3/2 quasiparticles with large topological charges. These unconventional fermions generate symmetry-protected topological surface states and underscore the nontrivial topology of the normal state. Symmetry analysis based on the Ginzburg-Landau theory suggests a loop-supercurrent-ordered superconducting state, yielding a full gap alongside spontaneous TRS breaking. The coexistence of TRS-breaking superconductivity and chiral multifold fermions identifies Ag₂Pd₃S as a platform for realizing intrinsic superconducting diode effects and chirality-induced spin selectivity, offering a transformative pathway toward dissipationless topological quantum technologies.