The objective investigation of the dynamic properties of vocal fold vibrations demands the recording and further quantitative analysis of laryngeal high-speed video (HSV). Quantification of the vocal fold vibration patterns requires as a first step the segmentation of the glottal area within each video frame from which the vibrating edges of the vocal folds are usually derived. Consequently, the outcome of any further vibration analysis depends on the quality of this initial segmentation process. In this work we propose for the first time a procedure to fully automatically segment not only the time-varying glottal area but also the vocal fold tissue directly from laryngeal high-speed video (HSV) using a deep Convolutional Neural Network (CNN) approach. Eighteen different Convolutional Neural Network (CNN) network configurations were trained and evaluated on totally 13,000 high-speed video (HSV) frames obtained from 56 healthy and 74 pathologic subjects. The segmentation quality of the best performing Convolutional Neural Network (CNN) model, which uses Long Short-Term Memory (LSTM) cells to take also the temporal context into account, was intensely investigated on 15 test video sequences comprising 100 consecutive images each. As performance measures the Dice Coefficient (DC) as well as the precisions of four anatomical landmark positions were used. Over all test data a mean Dice Coefficient (DC) of 0.85 was obtained for the glottis and 0.91 and 0.90 for the right and left vocal fold (VF) respectively. The grand average precision of the identified landmarks amounts 2.2 pixels and is in the same range as comparable manual expert segmentations which can be regarded as Gold Standard. The method proposed here requires no user interaction and overcomes the limitations of current semiautomatic or computational expensive approaches. Thus, it allows also for the analysis of long high-speed video (HSV)-sequences and holds the promise to facilitate the objective analysis of vocal fold vibrations in clinical routine. The here used dataset including the ground truth will be provided freely for all scientific groups to allow a quantitative benchmarking of segmentation approaches in future.