We report direct measurement of the center-of-mass diffusion coefficient, D, of uncharged flexible linear chains adsorbed at the solid-liquid interface at dilute surface coverage. We find D similar to N-3/2 (AT is degree of polymerization) when N was varied by more than an order of magnitude (N = 48, 113, 244, 456, and 693) and the scatter of the data was low. The experimental system was poly(ethylene glycol), PEG, adsorbed from dilute aqueous solution onto a self-assembled hydrophobic monolayer, condensed octadecyltriethoxysilane. The method of measurement was fluorescence correlation spectroscopy of a rhodamine green derivative dye that was end-attached to one sole end of the adsorbed PEG chains. The observed scaling implies the diffusion time tau similar to N-3 if R-g similar to N-3/4 as expected for a chain in good solvent in two dimensions (R-g is the radius of gyration), but a variety of other theoretical approaches to describe the dynamical scaling are also plausible. The multiplicity of plausible dynamical transport scenarios is compounded by the fact that polymer diffusion is sensitive to chain conformation on the surface which is not directly observable. Various theoretical scenarios are explored, and the need for new experiments, theory, and computer simulation studies to allow definitive interpretation of this observation of simple and clean fractional power law scaling is emphasized.