A central question in sequence comparison is the statistical significance of an observed similarity. For local alignment containing gaps to optimize sequence similarity this problem has so far not been solved mathematically. Using as a basis the Chen-Stein theory of Poisson approximation, we present a practical method to approximate the probability that a local alignment score is a result of chance alone. For a set of similarity scores and gap penalties only one simulation of random alignments needs to be calculated to derive the key information allowing us to estimate the significance of any alignment calculated under this setting. We present applications to data base searching and the analysis of pairwise and self-comparisons of proteins.