This paper describes an interactive approach to the identification of coronary arteries in 3D angiography images. The approach is based on a novel multiple hypothesis tracking methodology which is complemented with a standard minimal path search, and it allows for a complete segmentation with little manual labor. When evaluated using the 3D CT angiography data supplied with the MICCAI'08 workshop 3D Segmentation in the Clinic: A Grand Challenge II, 98% of the target coronary arteries could be segmented in about 5 minutes per data set with the same spatial accuracy achieved in manual segmentations by human experts.