Contemporary large language model (LLM) chat systems treat conversation history as an immutable sequence of turns that defines the model's working context. However, user intent in real interactions is not static: it evolves through correction, refinement, and shifting constraints. This mismatch between dynamic intent and static transcripts can result in context pollution, where outdated or irrelevant information persists and continues to influence subsequent responses. We introduce mutable transcripts, a new interaction paradigm that enables users to revise prior turns through natural language edit requests, allowing the conversation history itself to be updated rather than appended. This reframes the transcript from a passive record into an editable representation of conversational state. We present a working prototype that integrates transcript-level revision into a standard chat interface and evaluate its feasibility through a controlled user study (n=17) and an illustrative transcript analysis of representative interaction scenarios. Participants significantly preferred mutable transcripts over standard chat across measures of clarity, confidence, and ease of use, with reduced intent to restart conversations. Transcript analysis of representative user study conversations shows that mutable transcripts can reduce conversation length and eliminate obsolete retained context. These findings provide initial evidence that user-driven revision of conversational history can improve interaction quality and help maintain a more current representation of user intent. The source code and prototype can be accessed at https://github.com/QxLabIreland/ReChat

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