We present a Recurrent Neural Network using LSTM (Long Short Term Memory) that is capable of modeling and predicting Local Field Potentials. We train and test the network on real data recorded from epilepsy patients. We construct networks that predict multi-channel LFPs for 1, 10, and 100 milliseconds forward in time. Our results show that prediction using LSTM outperforms regression when predicting 10 and 100 millisecond forward in time.