This paper presents our first results using Deep Neural Networks for surface electromyographic (EMG) speech synthesis. The proposed approach enables a direct mapping from EMG signals captured from the articulatory muscle movements to the acoustic speech signal. Features are processed from multiple EMG channels and are fed into a feed forward neural network to achieve a mapping to the target acoustic speech output. We show that this approach is feasible to generate speech output from the input EMG signal and compare the results to a prior mapping technique based on Gaussian mixture models. The comparison is conducted via objective Mel-Cepstral distortion scores and subjective listening test evaluations. It shows that the proposed Deep Neural Network approach gives substantial improvements for both evaluation criteria.