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LLMs are becoming increasingly capable and widespread. Consequently, the potential and reality of their misuse is also growing. In this work, we address the problem of detecting LLM-generated text that is not explicitly declared as such. We present a novel, general-purpose, and supervised LLM text detector, SElected-Next-Token tRAnsformer (SENTRA). SENTRA is a Transformer-based encoder leveraging selected-next-token-probability sequences and utilizing contrastive pre-training on large amounts of unlabeled data. Our experiments on three popular public datasets across 24 domains of text demonstrate SENTRA is a general-purpose classifier that significantly outperforms popular baselines in the out-of-domain setting.