Both theoretical and applied economics have a great deal to say about many aspects of the firm, but the literature on the extinctions, or demises, of firms is very sparse. We use a publicly available data base covering some 6 million firms in the US and show that the underlying statistical distribution which characterises the frequency of firm demises - the disappearances of firms as autonomous entities - is closely approximated by a power law. The exponent of the power law is, intriguingly, close to that reported in the literature on the extinction of biological species.