We report on muon-spin relaxation measurements of the 4f(2)-based heavy-fermion superconductor filled-skutterudite Pr(Os4Sb12. The results reveal the spontaneous appearance of static internal magnetic fields below the superconducting transition temperature, providing unambiguous evidence for the breaking of time-reversal symmetry in the superconducting state. A discussion is made on which of the spin or orbital component of Cooper pairs carries a nonzero momentum.