How do we know which grammatical error correction (GEC) system is best? A number of metrics have been proposed over the years, each motivated by weaknesses of previous metrics; however, the metrics themselves have not been compared to an empirical gold standard grounded in human judgments. We conducted the first human evaluation of GEC system outputs, and show that the rankings produced by metrics such as MaxMatch and I-measure do not correlate well with this ground truth. As a step towards better metrics, we also propose GLEU, a simple variant of BLEU, modified to account for both the source and the reference, and show that it hews much more closely to human judgments.