Sr2RuO4 is an oxide metal which becomes superconducting at 1.5 K. In conventional superconductors, the electron (Cooper) pairs responsible for superconductivity have zero angular momentum, and zero net spin. In contrast, Sr2RuO4 is highly unconventional because the electrons form Cooper pairs with an angular momentum L=1. In addition, the spins of the paired electrons form a triplet spin state. Soon after the discovery of superconductivity in Sr2RuO4, muon spin resonance showed that additional magnetic moments appears on entering the superconducting state. The exact symmetry of the superconducting state of Sr2RuO4 is still hotly debated, but it seems impossible to reconcile the existence of these moments directly with the superconductivity. We therefore propose to search directly for spin density wave order. The presence of this type of order would explain this long standing mystery.