We derive total (atomic + molecular) hydrogen densities in giant molecular clouds (GMCs) in the nearby spiral galaxy M33 using a method that views the atomic hydrogen near regions of recent star formation as the product of photodissociation. Far-ultraviolet (FUV) photons emanating from a nearby OB association produce a layer of atomic hydrogen on the surfaces of nearby GMCs. Our approach provides an estimate of the total hydrogen density in these GMCs from observations of the excess FUV emission that reaches the GMC from the OB association and of the excess 21-cm radio HI emission produced after these FUV photons convert H2 into HI on the GMC surface. The method provides an alternative approach to the use of CO emission as a tracer of H2 in GMCs and is especially sensitive to a range of densities well below the critical density for CO(1-0) emission.