We propose two supervised methods for people counting using an overhead fisheye camera. As opposed to standard cameras, fisheye cameras offer a large field of view and, when mounted overhead, reduce occlusions. However, methods developed for standard cameras perform poorly on fisheye images since they do not account for the radial image geometry. Furthermore, no large-scale fisheye-image datasets with radially-aligned bounding box annotations are available for training. We adapt YOLOv3 trained on standard images for people counting in fisheye images. In one method, YOLOv3 is applied to 24 rotated, overlapping windows and the results are post-processed to produce a people count. In another method, YOLOv3 is applied to windows of interest extracted by background subtraction. For evaluation, we collected and annotated an indoor fisheye-image dataset that we make public. Experiments on this dataset show that our methods reduce the people counting MAE of two natural benchmarks by over 60%.