This paper presents a robust algorithm for cosmic ray rejection in single CCD exposures, based on a variation of Laplacian edge detection. Traditional methods rely on contrast between cosmic rays and their surroundings, but can fail when the Point Spread Function (PSF) is smaller than the cosmic rays. The new algorithm identifies cosmic rays by the sharpness of their edges, reliably distinguishing them from poorly sampled point sources. The algorithm uses the Laplacian of a 2-D Gaussian function to detect edges in images. The Laplacian is sensitive to sharp edges, making it effective for detecting cosmic rays. The algorithm first subsamples the image, convolves it with the Laplacian kernel, and then sets negative values to zero to retain cosmic ray affected pixels. The image is then resampled to its original resolution. The algorithm is implemented in the program LA.Cosmic, which can be obtained from the author's website. It is robust, requiring few user-defined parameters, and can handle cosmic rays of arbitrary size. The algorithm is tested on various data sets, including spectroscopic and imaging data, and performs well in removing cosmic rays from Hubble Space Telescope (HST) W FPC2 data. The algorithm is also effective in removing sampling flux from images, distinguishing between cosmic rays and point sources by their symmetry. It uses a noise model to identify cosmic rays by comparing pixel values to expected noise levels. The algorithm is particularly effective for undersampled data, where the parameter f_lim is set to a higher value to discriminate between cosmic rays and point sources. The algorithm is tested on real and artificial data sets, consistently producing very good results. It is particularly effective in removing cosmic rays from HST W FPC2 data, which are notoriously difficult to remove due to their large number and the undersampling of the PSF. The algorithm is also effective in spectroscopic data, where it can fit and subtract sky lines and object spectra before convolution with the Laplacian kernel. The algorithm is able to remove arbitrarily large cosmic rays and is robust to variations in sampling and S/N ratio.This paper presents a robust algorithm for cosmic ray rejection in single CCD exposures, based on a variation of Laplacian edge detection. Traditional methods rely on contrast between cosmic rays and their surroundings, but can fail when the Point Spread Function (PSF) is smaller than the cosmic rays. The new algorithm identifies cosmic rays by the sharpness of their edges, reliably distinguishing them from poorly sampled point sources. The algorithm uses the Laplacian of a 2-D Gaussian function to detect edges in images. The Laplacian is sensitive to sharp edges, making it effective for detecting cosmic rays. The algorithm first subsamples the image, convolves it with the Laplacian kernel, and then sets negative values to zero to retain cosmic ray affected pixels. The image is then resampled to its original resolution. The algorithm is implemented in the program LA.Cosmic, which can be obtained from the author's website. It is robust, requiring few user-defined parameters, and can handle cosmic rays of arbitrary size. The algorithm is tested on various data sets, including spectroscopic and imaging data, and performs well in removing cosmic rays from Hubble Space Telescope (HST) W FPC2 data. The algorithm is also effective in removing sampling flux from images, distinguishing between cosmic rays and point sources by their symmetry. It uses a noise model to identify cosmic rays by comparing pixel values to expected noise levels. The algorithm is particularly effective for undersampled data, where the parameter f_lim is set to a higher value to discriminate between cosmic rays and point sources. The algorithm is tested on real and artificial data sets, consistently producing very good results. It is particularly effective in removing cosmic rays from HST W FPC2 data, which are notoriously difficult to remove due to their large number and the undersampling of the PSF. The algorithm is also effective in spectroscopic data, where it can fit and subtract sky lines and object spectra before convolution with the Laplacian kernel. The algorithm is able to remove arbitrarily large cosmic rays and is robust to variations in sampling and S/N ratio.