We explore the use of neural networks trained with dropout in predicting epileptic seizures from electroencephalographic data (scalp EEG). The input to the neural network is a 126 feature vector containing 9 features for each of the 14 EEG channels obtained over 1-second, non-overlapping windows. The models in our experiments achieved high sensitivity and specificity on patient records not used in the training process. This is demonstrated using leave-one-out-cross-validation across patient records, where we hold out one patient's record as the test set and use all other patients' records for training; repeating this procedure for all patients in the database.