Entropy estimates for natural languages are useful for a number of reasons. For example, they can be used to estimate the length of a translated text or the amount of text required to make a brute-force attack on an encrypted message feasible. This paper briefly reviews the development of techniques for entropy estimation and then applies modern techniques to Irish text. We believe this addresses a gap in the literature giving an entropy estimate for the Irish language. We discuss our results in the context of entropy estimates for equivalent English text.