The single helical Fermi surface on the surface state of three-dimensional topological insulator Bi2Se3 is constrained by the time-reversal invariant bulk topology to possess a spin-singlet superconducting pairing symmetry. In fact, the Cu-doped and pressure-tuned superconducting Bi2Se3 show no evidence of the time-reversal symmetry (TRS) breaking. We report on the detection of the TRS breaking in the topological superconductor Sr0.1Bi2Se3, probed by zero-field mu SR measurements. The TRS breaking provides strong evidence for the existence of a spin-triplet pairing state. The existence of TRS breaking is also verified by longitudinal-field mu SR measurements, which negates the possibility of magnetic impurities as the source of TRS breaking. The temperature-dependent superfluid density deduced from transverse-field mu SR measurements yields nodeless superconductivity with low superconducting carrier density and penetration depth lambda = 1622(134) nm. From the microscopic theory of unconventional pairing, we find that such a fully gapped spin-triplet pairing channel is promoted by the complex interplay between the structural hexagonal warping and higher order Dresselhaus spinorbit-coupling terms. Based on Ginzburg-Landau analysis, we delineate the mixing of singlet- to triplet-pairing symmetry as the chemical potential is tuned far above from the Dirac cone. Our observation of such spontaneous TRS breaking chiral superconductivity on a helical surface state, protected by the TRS invariant bulk topology, can open avenues for interesting research and applications.