A novel data driven approach to batch process monitoring is presented, which combines the k-Nearest Neighbour rule with the dynamic time warping (DTW) distance. This online method (DTW-NN) calculates the DTW distance between an ongoing batch, and each batch in a reference database of batches produced under normal operating conditions (NOC). The sum of the k smallest DTW distances is monitored. If a fault occurs in the ongoing batch, then this distance increases and an alarm is generated. The monitoring statistic is easy to interpret, being a direct measure of similarity of the ongoing batch to its nearest NOC predecessors and the method makes no distributional assumptions regarding normal operating conditions. DTW-NN is applied to four extensive datasets from simulated batch production of penicillin, and tested on a wide variety of fault types, magnitudes and onset times. Performance of DTW-NN is contrasted with a benchmark multiway PCA approach, and DTW-NN is shown to perform particularly well when there is clustering of batches under NOC.