In order to safely navigate and orient in their local surroundings autonomous systems need to rapidly extract and persistently track visual features from the environment. While there are many algorithms tackling those tasks for traditional frame-based cameras, these have to deal with the fact that conventional cameras sample their environment with a fixed frequency. Most prominently, the same features have to be found in consecutive frames and corresponding features then need to be matched using elaborate techniques as any information between the two frames is lost. We introduce a novel method to detect and track line structures in data streams of event-based silicon retinae [also known as dynamic vision sensors (DVS)]. In contrast to conventional cameras, these biologically inspired sensors generate a quasicontinuous stream of vision information analogous to the information stream created by the ganglion cells in mammal retinae. All pixels of DVS operate asynchronously without a periodic sampling rate and emit a so-called DVS address event as soon as they perceive a luminance change exceeding an adjustable threshold. We use the high temporal resolution achieved by the DVS to track features continuously through time instead of only at fixed points in time. The focus of this work lies on tracking lines in a mostly static environment which is observed by a moving camera, a typical setting in mobile robotics. Since DVS events are mostly generated at object boundaries and edges which in man-made environments often form lines they were chosen as feature to track. Our method is based on detecting planes of DVS address events in x-y-t-space and tracing these planes through time. It is robust against noise and runs in real time on a standard computer, hence it is suitable for low latency robotics. The efficacy and performance are evaluated on real-world data sets which show artificial structures in an office-building using event data for tracking and frame data for ground-truth estimation from a DAVIS240C sensor.