Large language models are increasingly deployed as advisors whose objective is not aligned with the user's: recommenders optimize for engagement, sales assistants for purchases, negotiation agents for concessions. Whether such advisors stay truthful when honesty conflicts with their own payoff is a core alignment-evaluation question. We turn the canonical Crawford-Sobel cheap-talk model into a pre-specified benchmark for LLM honesty under preference misalignment. Cheap-talk theory predicts neither full revelation nor silence but coarse monotone partitions, with fewer informative intervals as preference conflict grows. A sender observes a state omega in [0,1], wants the receiver's action near omega+b, and sends one costless message to a receiver whose ideal action is omega. The design uses 5 bias levels, 3 prompt frames, a fixed low-temperature setting, and 200 states per cell: 12,000 sender calls. For the positive-bias grid b in {0.01,0.04,0.08,0.12} the exact most-informative partition sizes are 7,4,3,2, with oracle normalized mutual information 0.5294, 0.3268, 0.2205, 0.1829. Running the full design on four instruction-tuned models (GPT-4o, Claude Sonnet 4.5, Gemini 2.5 Flash-Lite, Llama-3.3-70B), we find all four over-reveal relative to the most-informative equilibrium by 1.8 to 4.2x: normalized mutual information stays at 0.78-0.94 where the oracle prescribes 0.18-0.53. Informativeness declines with bias as predicted but never approaches the strategic optimum; rather than coarse partitions, models show near-full revelation with a constant upward offset tracking their bias (linear exaggeration). Payoff-maximizing versus honesty framing has negligible effect. A decoder ablation shows the finding is recoverable only when the receiver reads the sender's stated number: an embedding-only decoder mis-reads the same data as near-babbling.