This paper presents GorillaVision, an open-set re-identification system for gorillas in the wild. Open-set re-identification is crucial to identify and track individual gorillas the system may not have previously encountered, thereby enhancing our understanding of gorilla behavior and population dynamics in dynamically changing wild environments. The system adopts a two-stage approach, in which gorilla faces are first detected with a YOLOv7 detector and subsequently classified with a custom neural network model. The classification model is based on a pre-trained Vision Transformer, which is fine-tuned with Triplet Loss to compute embeddings of gorilla faces. Such embeddings can be relied upon to obtain a similarity measure between gorilla faces and thus also between individual gorillas. Classification is then performed on these embeddings with a k-nearest neighbors algorithm. We evaluate our method on two heterogeneous datasets and show that our approach yields minor gains over the state-of-the-art YOLO detector in a closed-set scenario. In an open-set scenario, our model can deliver high-quality results with an accuracy of 60 to 90%, depending on the dataset quality and the number of individuals.