Benford's Law owes its discovery to the ``Grubby Pages Hypothesis,'' a nineteenth century observation that the beginning pages of logarithm books were dirtier than the last few pages, implying that scientists referenced the values toward the front of the books more frequently. This peculiarity led to the hypothesis that the significant digits of many data sets describing the physical world are not uniformly distributed, but distributed in a way that favors smaller digits.Benford's Law takes this hypothesis further by providing a probability mass function for combinations of significant digits. While the law may be obscure, it is well established that many common data sets like stock prices, tax data, and census statistics are described by Benford's Law. Over the past few months, I have worked to establish that many dynamical systems are consistent with Benford's Law. Numerical evidence for this is overwhelming and easy to generate. I also have some analytical results that are convincing, but limited in scope.