  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 breaking. We report on the detection of the time
reversal symmetry (TRS) breaking in the topological superconductor Sr0.1Bi2Se3
, probed by zero-field (ZF) {\mu}SR measurements. The TRS breaking provides
strong evidence for the existence of spin-triplet pairing state. The
temperature dependent super-fluid density deduced from transverse-field (TF)
{\mu}SR measurement 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 spin-orbit 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 new avenues for interesting research and applications.
