An approximate expression for the probability distribution of the age of a neutral allele as a function of its frequency is derived for a population undergoing arbitrary changes in population size. A simple maximum–likelihood estimator of allele age based on frequency is also obtained. The distribution of allele age, combined with a model predicting the extent of intra–allelic variability generated by mutation and recombination, leads to a statistical test of whether a rare allele has experienced natural selection. The test is based on finding whether there is too little or too much intra–allelic variability to be consistent with the observed frequency. The test is applied to the locus, BRCA1, associated with early–onset breast cancer in humans and shows that two common disease–associated alleles (5382insC and 185delAG) appear to have been subject to natural selection.