High-T-c cuprates, iron pnictides, organic BEDT and TMTSF, alkali-doped C-60, and heavy-fermion systems have superconducting states adjacent to competing states exhibiting static antiferromagnetic or spin density wave order. This feature has promoted pictures for their superconducting pairing mediated by spin fluctuations. Sr2RuO4 is another unconventional superconductor which almost certainly has a p-wave pairing. The absence of known signatures of static magnetism in the Sr-rich side of the (Ca, Sr) substitution space, however, has led to a prevailing view that the superconducting state in Sr2RuO4 emerges from a surrounding Fermi-liquid metallic state. Using muon spin relaxation and magnetic susceptibility measurements, we demonstrate here that (Sr, Ca)(2)RuO4 has a ground state with static magnetic order over nearly the entire range of (Ca, Sr) substitution, with spin-glass behaviour in Sr1:5Ca0:5RuO4 and Ca1.5Sr0.5RuO4. The resulting new magnetic phase diagram establishes the proximity of superconductivity in Sr2RuO4 to competing static magnetic order.