Polymer dynamics are of fundamental importance in materials science, biotechnology, and medicine. However, very little is known about the kinetics of partitioning of flexible polymer molecules into pores of nanometer dimensions. We employed electrical recording to probe the partitioning of single poly(ethylene glycol) (PEG) molecules, at concentrations near the dilute regime, into the transmembrane β-barrel of individual protein pores formed from staphylococcal α-hemolysin (αHL). The interactions of the α-hemolysin pore with the PEGs (M_w 940–6000Da) fell into two classes: short-duration events (τ ∼ 20μs), ∼85% of the total, and long-duration events (τ ∼ 100μs), ∼15% of the total. The association rate constants (k_on) for both classes of events were strongly dependent on polymer mass, and values of k_on ranged over two orders of magnitude. By contrast, the dissociation rate constants (k_off) exhibited a weak dependence on mass, suggesting that the polymer chains are largely compacted before they enter the pore, and do not decompact to a significant extent before they exit. The values of k_on and k_off were used to determine partition coefficients (Π) for the PEGs between the bulk aqueous phase and the pore lumen. The low values of Π are in keeping with a negligible interaction between the PEG chains and the interior surface of the pore, which is independent of ionic strength. For the long events, values of Π decrease exponentially with polymer mass, according to the scaling law of Daoud and de Gennes. For PEG molecules larger than ∼5 kDa, Π reached a limiting value suggesting that these PEG chains cannot fit entirely into the β-barrel.