Although the properties of most superconducting materials are well des
cribed by the theory(1) of Bardeen, Cooper and Schrieffer (BCS), consi
derable effort has been devoted to the search for exotic superconducti
ng systems in which BCS theory does not apply. The transition to the s
uperconducting state in conventional BCS superconductors involves the
breaking of gauge symmetry only, whereby the wavefunction describing t
he Cooper pairs-the paired electron states responsible for superconduc
tivity-adopt a definite phase. In contrast, a signature of an unconven
tional superconducting state is the breaking of additional symmetries(
2), which can lead to anisotropic pairing (such as the 'd-wave' symmet
ry observed in the copper oxide superconductors) and the presence of m
ultiple superconducting phases (as seen in UPt3 and analogous behaviou
r in superfluid He-3; refs 3-5). Here we report muon spin-relaxation m
easurements on the superconductor Sr2RuO4 that reveal the spontaneous
appearance of an internal magnetic held below the transition temperatu
re: the appearance of such a held indicates that the superconducting s
tate in this material is characterized by the breaking of time-reversa
l symmetry. These results, combined with other symmetry considerations
, suggest that superconductivity in Sr2RuO4 is of 'p-wave' (odd-parity
) type, analogous to superfluid He-3.