Single-molecule Förster resonance energy transfer (FRET) experiments were performed on the enzyme RNase H specifically labeled with a FRET dye pair and diffusing freely in solutions containing between 0 and 6 M of the chemical denaturant GdmCl. We measured FRET efficiency histograms with high statistical accuracy to identify the well-known folding intermediate of RNase H, which escaped observation in our previous smFRET studies on immobilized preparations. Even with excellent data statistics, a folding intermediate is not obvious from the raw data. However, it can be uncovered by a global fitting procedure applied to the FRET histograms at all 22 GdmCl concentrations, in which a number of parameters were constrained. Most importantly, the fractional populations of the folded, unfolded and intermediate states were coupled by assuming the Boltzmann relation and a linear dependence of the free energies on the GdmCl concentration. The analysis not only resolves the apparent discrepancy with other data on RNase H, but yields free energy differences between the three populations in agreement with literature data. In addition, it removes t ... mehrhe strong and unexplained broadening of the unfolded-state distribution in the transition region that was seen earlier in the two-state analysis.