Precise delineation of organs at risk (OAR) is a crucial task in radiotherapy treatment planning, which aims at delivering high dose to the tumour while sparing healthy tissues. In recent years algorithms showed high performance and the possibility to automate this task for many OAR. However, for some OAR precise delineation remains challenging. The esophagus with a versatile shape and poor contrast is among these structures. To tackle these issues we propose a 3D fully (convolutional neural network (CNN) driven random walk (RW) approach to automatically segment the esophagus on CT. First, a soft probability map is generated by the CNN. Then an active contour model (ACM) is fitted on the probability map to get a first estimation of the center line. The outputs of the CNN and ACM are then used in addition to CT Hounsfield values to drive the RW. Evaluation and training was done on 50 CTs with peer reviewed esophagus contours. Results were assessed regarding spatial overlap and shape similarities. The generated contours showed a mean Dice coefficient of 0.76, an average symmetric square distance of 1.36 mm and an average Hausdorff distance of 11.68 compared to the reference. These figures translate into a very good agreement with the reference contours and an increase in accuracy compared to other methods. We show that by employing a CNN accurate estimations of esophagus location can be obtained and refined by a post processing RW step. One of the main advantages compared to previous methods is that our network performs convolutions in a 3D manner, fully exploiting the 3D spatial context and performing an efficient and precise volume-wise prediction. The whole segmentation process is fully automatic and yields esophagus delineations in very good agreement with the used gold standard, showing that it can compete with previously published methods.