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.