Text classification is a widely studied problem, and it can be considered solved for some domains and under certain circumstances. There are scenarios, however, that have received little or no attention at all, despite its relevance and applicability. One of such scenarios is early text classification, where one needs to know the category of a document by using partial information only. A document is processed as a sequence of terms, and the goal is to devise a method that can make predictions as fast as possible. The importance of this variant of the text classification problem is evident in domains like sexual predator detection, where one wants to identify an offender as early as possible. This paper analyzes the suitability of the standard naive Bayes classifier for approaching this problem. Specifically, we assess its performance when classifying documents after seeing an increasingly number of terms. A simple modification to the standard naive Bayes implementation allows us to make predictions with partial information. To the best of our knowledge naive Bayes has not been used for this purpose before. Throughout an extensive experimental evaluation we show the effectiveness of the classifier for early text classification. What is more, we show that this simple solution is very competitive when compared with state of the art methodologies that are more elaborated. We foresee our work will pave the way for the development of more effective early text classification techniques based in the naive Bayes formulation.