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Tokenization efficiency plays a critical role in the performance and cost of large language models (LLMs), yet most models rely on static tokenizers optimized on general-purpose corpora. These tokenizers' fixed vocabularies often fail to adapt to domain-or language-specific inputs, leading to longer token sequences and higher computational costs. We introduce zip2zip, a novel method for achieving context-adaptive tokenization in LLMs at inference time. Leveraging an online data compression algorithm (Lempel-Ziv-Welch), zip2zip dynamically expands its active vocabulary at inference time by continuously replacing fragmented token sequences with more compact hypertokens, which it can immediately output during generation. zip2zip consists of three key components: (1) a tokenizer based on Lempel-Ziv-Welch compression that incrementally merges co-occurring tokens into reusable hypertokens on the fly; (2) a dynamic embedding (and unembedding) layer that computes embeddings for newly formed hypertokens at runtime; and (3) a variant of autoregressive language modeling that pretrains the model to handle hypertokenized, compressed text sequences as inputs and outputs. We show that an existing LLM can be uptrained for zip2zip in 10 GPU-hours via parameter-efficient finetuning. The resulting LLM performs test-time adaptation, learning to use hypertokens in unseen contexts and reducing input and output tokens by 15-40%.