In recent years there has been intense experimental activity to observe solid metallic hydrogen. Wigner and Huntington predicted that under extreme pressures insulating molecular hydrogen would dissociate and transition to atomic metallic hydrogen. Recently Dalladay-Simpson, Howie, and Gregoryanz reported a phase transition to an insulating phase in molecular hydrogen at a pressure of 325 GPa and 300 K. Because of its scientific importance we have scrutinized their experimental evidence to determine if their claim is justified. Based on our analysis, we conclude that they have misinterpreted their data: there is no evidence for a phase transition at 325 GPa.