Experimental observations suggest that contour integration may take place in V1. However, there has yet to be a model of contour integration that uses only known V1 elements, operations, and connection patterns. This article introduces such a model, using orientation selective cells, local cortical circuits, and horizontal intracortical connections. The model is composed of recurrently connected excitatory neurons and inhibitory interneurons, receiving visual input via oriented receptive fields resembling those found in primary visual cortex. Intracortical interactions modify initial activity patterns from input, selectively amplifying the activities of edges that form smooth contours in the image. The neural activities produced by such interactions are oscillatory and edge segments within a contour oscillate in synchrony. It is shown analytically and empirically that the extent of contour enhancement and neural synchrony increases with the smoothness, length, and closure of contours, as observed in experiments on some of these phenomena. In addition, the model incorporates a feedback mechanism that allows higher visual centers selectively to enhance or suppress sensitivities to given contours, effectively segmenting one from another. The model makes the testable prediction that the horizontal cortical connections are more likely to target excitatory (or inhibitory) cells when the two linked cells have their preferred orientation aligned with (or orthogonal to) their relative receptive field center displacements.