Precision farming robots, which target to reduce the amount of herbicides that need to be brought out in the fields, must have the ability to identify crops and weeds in real time to trigger weeding actions. In this paper, we address the problem of CNN-based semantic segmentation of crop fields separating sugar beet plants, weeds, and background solely based on RGB data. We propose a CNN that exploits existing vegetation indexes and provides a classification in real time. Furthermore, it can be effectively re-trained to so far unseen fields with a comparably small amount of training data. We implemented and thoroughly evaluated our system on a real agricultural robot operating in different fields in Germany and Switzerland. The results show that our system generalizes well, can operate at around 20Hz, and is suitable for online operation in the fields.