Intramolecular dynamics in the denatured state of a protein are of importance for protein folding. Native-like contact formation within the ensemble of denatured conformations of a protein may guide its transformation towards the native conformation. The efficiency of folding is thus dependent on the diffusion of chain fragments, which facilitates contact formation. Herein we investigate intramolecular diffusion of denatured molecules of the small two-state-folding protein L with fluorescence correlation spectroscopy (FCS). We utilize the specific quenching of the fluorescence of the oxazine dye Atto655 labeling a cysteine at position 64 (the C-terminus of the protein) by the side chain of a tryptophan at position 47. FCS measurements allow us to probe processes ranging in timescales from tens of nanoseconds to seconds. Two fast photophysical processes can be distinguished in the fluorescence correlation curves. The slower of the two is found to be due to triplet dynamics, while the faster process is attributed to the quenching of the Atto655 by the tryptophan upon transient ground-state complex formation. We study the dependence of the intrachain dynamics of the denatured protein on the concentration of the denaturant guanidinium chloride (GdmCl), and extract complex association and dissociation rates. While the dissociation rate does not depend on the denaturant, the association rate decreases as denaturant concentration is increased from 3 to 7 M GdmCl. This decrease in contact formation rate tracks the expansion of denatured protein L, measured in our previous work. Thus, the intramolecular diffusion coefficient calculated from the results is found to be essentially independent of the denaturant concentration over this range, even as the protein expands by more than 20 %.