We propose an algorithm for segmentation of grayscale images. Our algorithm computes a solution to the convex, unconstrained minimization problem proposed by T. Chan, S. Esedog̅lu, and M. Nikolova, which is closely related to the Chan-Vese level set algorithm for the Mumford-Shah segmentation model. Up to now this problem has been solved with a gradient descent method. Our approach is a quasi-Newton method based on the lagged diffusivity algorithm of C. Vogel and M. Oman for minimizing the total-variation functional for image denoising of S, Osher, W. Rudin, and E. Fatemi. Our results show that our algorithm requires a much smaller number of iterations and less time to converge than gradient descent, and is able to segment noisy images correctly.