To plan safe and comfortable trajectories for automated vehicles on highways, accurate predictions of traffic situations are needed. So far, a lot of research effort has been spent on detecting lane change maneuvers rather than on estimating the point in time a lane change actually happens. In practice, however, this temporal information might be even more useful. This paper deals with the development of a system that accurately predicts the time to the next lane change of surrounding vehicles on highways using long short-term memory-based recurrent neural networks. An extensive evaluation based on a large real-world data set shows that our approach is able to make reliable predictions, even in the most challenging situations, with a root mean squared error around 0.7 seconds. Already 3.5 seconds prior to lane changes the predictions become highly accurate, showing a median error of less than 0.25 seconds. In summary, this article forms a fundamental step towards downstreamed highly accurate position predictions.