We perceive structure through a process of perceptual organization. Here we report a new perceptual organization phenomenon--the facilitation of visual grouping by global curvature. Observers viewed patterns that they perceived as organized into collections of curves. The patterns were perceptually ambiguous such that the perceived orientation of the patterns varied from trial to trial. When patterns were sufficiently dense and proximity was equated for the predominant perceptual alternatives, observers tended to perceive the organization with the greatest curvature. This effect is tantamount to "visual grouping by maximal curvature" and thus demonstrates an unprecedented effect of global structure on perceptual organization. We account for this result with a model that predicts the perceived organization of a pattern as function of its "nonaccidentality", which we define as the probability that it could have occurred by chance. Our findings demonstrate a novel relationship between the geometry of a pattern and the visual salience of global structure. (Contains 1 table and 4 figures.)