This book constitutes the First 3D Head and Neck Tumor Segmentation in PET/CT Challenge, HECKTOR 2020, which was held in conjunction with the 23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020, in Lima, Peru, in October 2020. The challenge took place virtually due to the COVID-19 pandemic. The 2 full and 8 short papers presented together with an overview paper in this volume were carefully reviewed and selected form numerous submissions. This challenge aims to evaluate and compare the current state-of-the-art methods for automatic head and neck tumor segmentation. In the context of this challenge, a dataset of 204 delineated PET/CT images was made available for training as well as 53 PET/CT images for testing. Various deep learning methods were developed by the participants with excellent results.