The success and the dominance of Hidden Markov Models (HMM) in the field of speech recognition, tends to extend also in the area of speech synthesis, since HMM provide a generalized statistical framework for efficient parametric speech modeling and generation. In this work, we describe the adaption, the implementation and the evaluation of the HMM speech synthesis framework for the case of the Greek language. Specifically, we detail on both the development of the training speech databases and the implementation issues relative to the particular characteristics of the Greek language. Experimental evaluation depicts that the developed text-to-speech system is capable of producing adequately natural speech in terms of intelligibility and intonation.