The well-established physical and mathematical principle of maximum entropy, interpreted as maximum uncertainty, is used to explain the observed dependence properties of the rainfall occurrence process, including the clustering behavior and persistence. The conditions used for the maximization of entropy are as simple as possible, i.e., that the rainfall processes is intermittent with dependent occurrences. Intermittency is quantified by the probability that a time interval is dry, and dependence is quantified by the probability that two consecutive intervals are dry. These two probabilities are used as constraints in a multiple-scale entropy maximization framework, which determines any conditional or unconditional probability of any sequence of dry and wet intervals at any timescale. Thus the rainfall occurrence process including its dependence structure is described by only two parameters. This dependence structure appears to be non-Markovian. Application of this theoretical framework to the rainfall data set of Athens indicates good agreement of theoretical predictions and empirical data at the entire range of scales for which probabilities dry and wet can be estimated (from one hour to several months).