The latest generation of spectral optical coherence tomography (OCT) scanners is able to image 3D cross-sectional volumes of the retina at a high resolution and high speed. These scans offer a detailed view of the structure of the retina. Automated segmentation of the vessels in these volumes may lead to more objective diagnosis of retinal vascular disease including hypertensive retinopathy, retinopathy of prematurity. Additionally, vessel segmentation can allow color fundus images to be registered to these 3D volumes, possibly leading to a better understanding of the structure and localization of retinal structures and lesions. In this paper we present a method for automatically segmenting the vessels in a 3D OCT volume. First, the retina is automatically segmented into multiple layers, using simultaneous segmentation of their boundary surfaces in 3D. Next, a 2D projection of the vessels is produced by only using information from certain segmented layers. Finally, a supervised, pixel classification based vessel segmentation approach is applied to the projection image. We compared the influence of two methods for the projection on the performance of the vessel segmentation on 10 optic nerve head centered 3D OCT scans. The method was trained on 5 independent scans. Using ROC analysis, our proposed vessel segmentation system obtains an area under the curve of 0.970 when compared with the segmentation of a human observer.