Since trees are a vital part of urban green infrastructure, automatic mapping of individual urban trees is becoming increasingly important for city management and planning. Although deep-learning-based object detection networks are the state-of-the-art in computer vision, their adaptation to individual tree detection in urban areas has scarcely been studied. Some existing works have employed 2D object detection networks for this purpose. However, these have used three-dimensional information only in the form of projected feature maps. In contrast, we exploited the full 3D potential of airborne laser scanning (ALS) point clouds by using a 3D neural network for individual tree detection. Specifically, a sparse convolutional network was used for 3D feature extraction, feeding both semantic segmentation and circular object detection outputs, which were combined for further increased accuracy. We demonstrate the capability of our approach on an urban topographic ALS point cloud with 10,864 hand-labeled ground truth trees. Our method achieved an average precision of 83% regarding the common 0.5 intersection over union criterion. 85% percent of the stems were found correctly with a precision of 88%, while tree area was covered by the individual tree detections with an F1 accuracy of 92%. Thereby, we outperformed traditional delineation baselines and recent detection networks.