In this study, we have shown with the use of UV-vis spectrophotometry and the constant wavelength synchronous fluorescence spectroscopy (CW-SFS) techniques that the pharmaceutical drug, chlorpromazine hydrochloride (CPZ), intercalates into the deoxyribonucleic acid (DNA) double helix by partial exchange with the Neutral Red (NR) molecular probe. We have also demonstrated that with the use of three-way data plots, it is clear that it is important to have well-defined methodology for the selection of the important CW-SFS method parameter, Deltalambda. Ad hoc selection of this parameter, or even that based on experience, can readily lead to serious errors, which subsequently can be transferred to the interpretation of results. The said three-way plots provide a straightforward diagrammatic method, which improves the selection process of a satisfactory value for Deltalambda. Finally, we used PARAFAC modeling to resolve the complex three-way CW-SFS data, which provided simultaneously the concentration information for the three reaction components, NR, CPZ and NR-DNA, for the system at equilibrium. This PARAFAC analysis indicated that the intercalation of the CPZ molecule into the DNA proceeds by exchanging with the NR probe, and can be attributed to two parallel reactions.