We have measured the emission line profiles in Hα from populations of HII regions in nearby spiral galaxies, and extracted their non-thermal line widths. These are supersonic for the more luminous regions. We infer from plots of line width, σ, against Hα luminosity, a set of regions in virial equilibrium, and derive their masses summing all known components. The virial masses are considerably larger. If this discrepancy, and the supersonic line widths, are due to the presence of magnetic fields, we can estimate their strengths at a few microgauss. Observational confirmation is clearly required.