The surface diffusion of potassium on Pd{111} has been studied with photoelectron emission microscopy (PEEM) for coverages up to one monolayer, The coverage dependence of the chemical diffusion coefficient is determined by analysis of the concentration profiles obtained from the PEEM images with the Boltzmann-Matano method. The diffusion coefficient, D, decreases with increasing coverage but a local maximum is found at a coverage of theta approximate to 0.5 ML. The values of D at low coverages (theta < 0.3 ML) agree well with those obtained in a previous investigation for theta approximate to 0.12 ML. The maximum in D is interpreted in terms of an order-disorder phase transition in the adsorbed layer.