We present a new, robust, computational procedure for tracking fluorescent markers in time-lapse microscopy. The algorithm is optimized for finding the time-trajectory of single particles in very noisy dynamic (two- or three-dimensional) image sequences. It proceeds in three steps. First, the images are aligned to compensate for the movement of the biological structure under investigation. Second, the particle's signature is enhanced by applying a Mexican hat filter, which we show to be the optimal detector of a Gaussian-like spot in 1/omega2 noise. Finally, the optimal trajectory of the particle is extracted by applying a dynamic programming optimization procedure. We have used this software, which is implemented as a Java plug-in for the public-domain ImageJ software, to track the movement of chromosomal loci within nuclei of budding yeast cells. Besides reducing trajectory analysis time by several 100-fold, we achieve high reproducibility and accuracy of tracking. The application of the method to yeast chromatin dynamics reveals different classes of constraints on mobility of telomeres, reflecting differences in nuclear envelope association. The generic nature of the software allows application to a variety of similar biological imaging tasks that require the extraction and quantitation of a moving particle's trajectory.