We adapt the greedy stack LSTM dependency parser of Dyer et al. (2015) to support a training-with-exploration procedure using dynamic oracles (Goldberg and Nivre, 2013) instead of assuming an error-free action history. This form of training, which accounts for model predictions at training time, improves parsing accuracies. We discuss some modifications needed in order to get training with exploration to work well for a probabilistic neural-network dependency parser.