Recent studies have shown that embedding similarity/dissimilarity measures between distributions in the variational level set framework can lead to effective object segmentation/tracking algorithms. In this connection, existing methods assume implicitly that the overlap between the distributions of image data within the object and its background has to be minimal. Unfortunately, such assumption may not be valid in many important applications. This study investigates an overlap prior, which embeds knowledge about the overlap between the distributions of the object and the background in level set tracking. It consists of evolving a curve to delineate the target object in the current frame. The level set curve evolution equation is sought following the maximization of a functional containing three terms: (1) an original overlap prior which measures the conformity of overlap between the nonparametric (kernel-based) distributions within the object and the background to a learned description, (2) a term which measures the similarity between a model distribution of the object and the sample distribution inside the curve, and (3) a regularization term for smooth segmentation boundaries. The Bhattacharyya coefficient is used as an overlap measure. Apart from leading to a method which is more versatile than current ones, the overlap prior speeds up significantly the curve evolution. Comparisons and results demonstrate the advantages of the proposed prior over related methods, and its usefulness in important applications such as the left ventricle tracking in magnetic resonance (MR) images.