We have measured nonphotochemical hole-burned spectra of the 5(and 6)-carboxy-X-rhodamine N-hydroxysuccinimidyl ester (RhSE) and the RhSE molecule bound to an oligonucleotide of three different sizes of guanosine (RhSE-nG) doped in polyvinyl alcohol (PVOH) films. The distribution of barrier heights of TLSs and the Linear electron-phonon coupling parameters are measured from temperature-annealing-cycling (TAG) hole-filled spectra. Binding an oligonucleotide to a RhSE decreases the hole-burning efficiency, which may be attributed to one degree of freedom of RhSE lost to the oligonucleotide. However, it has little effect on the spontaneous hole filling, the distribution of barrier heights, and the linear electron-phonon coupling. In addition, similar results observed for the burning efficiency, the distribution of barrier heights, and the linear electron-phonon coupling of various sizes of RhSE-nG/PVOH eliminate the possible effect of free volume produced by the large size of the oligonucleotide around the chromophore. These results, along with the identical frequency of satellite holes observed in these samples, also suggest that the chromophore sits outside the large group of the oligonucleotide. Therefore, we believe that binding an oligonucleotide to a chromophore has little effect on the configurational relaxation of chromophore-glass ensembles.