For some enzymes, virtually every substrate molecule that encounters the entrance to the active site proceeds to reaction, at low substrate concentrations. Such diffusion-limited enzymes display high apparent bimolecular rate constants ((kcat/KM)), which depend strongly upon solvent viscosity. Some experimental studies provide evidence that acetylcholinesterase falls into this category. Interestingly, the asymmetric charge distribution of acetylcholinesterase, apparent from the crystallographic structure, suggests that its electrostatic field accelerates the encounter of its cationic substrate, acetylcholine, with the entrance to the active site. Here we report simulations of the diffusion of substrate in the electrostatic field of acetylcholinesterase. We find that the field indeed guides the substrate to the mouth of the active site. The computed encounter rate constants depend upon the particular relative geometries of substrate and enzyme that are considered to represent successful encounters. With loose reaction criteria, the computed rates exceed those measured experimentally, but the rate constants vary appropriately with ionic strength. Although more restrictive reaction criteria lower the computed rates, they also lead to unrealistic variation of the rate constants with ionic strength. That these simulations do not agree well with experiment suggests that the simple diffusion model is incomplete. Structural fluctuations in the enzyme or events after the encounter may well contribute to rate limitation.