In addition to its importance for existing and potential applications, superconductivity [1] is one of the most interesting phenomena in condensed matter physics.Although most superconducting materials are well-described in the context of the Bardeen Cooper and Schrieffer (BCS) theory [2], considerable effort has been devoted to the search for exotic systems whose novel properties cannot be described by the BCS theory. Conventional superconductors break only gauge symmetry by selecting a definite phase for the Cooper pair wavefunction; a signature of an unconventional superconducting state is the breaking of additional symmetries [3].Evidence for such broken symmetries include anisotropic pairing (such as d-wave in the high-T c cuprates) and the presence of multiple superconducting phases (UPt 3 and superfluid 3 He[4]). We have performed muon spin relaxation measurements of Sr 2 RuO 4 and observe a spontaneous internal magnetic field appearing below T c . Our measurements indicate that the superconducting state in Sr 2 RuO 4 is characterized by broken time reversal symmetry which, when combined with symmetry considerations indicate that its superconductivity is of p-wave (odd-parity) type, analagous to superfluid 3 He. Despite the structural similarity with the high T c cuprates, the origin of the unconventional superconductivity in Sr 2 RuO 4 is fundamentally different in nature.Sr 2 RuO 4 , which is isostructural to the high-T c cuprate La 1.85 Sr 0.15 CuO 4 , is to date the only known layered perovskite superconductor which does not contain copper. Although first synthesized in the 50's, [5] its superconductivity was only found in 1994[6]; T c 's of early samples were roughly 0.7 K but have increased to T c = 1.5 K in recent high quality single crystals [7]. Despite its low transition temperature, Sr 2 RuO 4 is of great interest as there is growing evidence for an unconventional superconducting state. In this system, strong correlation effects enhance the effective mass seen in quantum oscillation [8] and Pauli spin susceptibility measurements, in the same way as in 3 He [9]. Combining this feature with Sr 2 RuO 4 's expected tendency to display ferromagnetic spin fluctuations, Rice and Sigrist [10], and later Baskaran [11] argued that the pairing in Sr 2 RuO 4 could be of odd parity (spin triplet) type.The strong suppression of the superconducting T c by even non-magnetic impurities suggests non-s-wave pairing [7]. Specific heat [12] and NMR 1/T 1 [13] measurements indicate the presence of a large residual density of states (RDOS) at low temperatures (well within the superconducting state); in high quality samples, this RDOS as T→ 0 seems to approach half of the normal state value. Several authors [14,15] have proposed so-called non-unitary p-wave superconducting states for Sr 2 RuO 4 to account for this RDOS as well as the absence of a Hebel-Slichter peak in NMR measurements [13]. A finite RDOS is not a unique signature of unconventional superconductivity; for example it is observed in so-called gapless sup...