We consider coverless steganography where a Large Language Model (LLM) is used to generate stego-texts in combination with arithmetic coding. An efficient method should embed secret bits in as few language tokens as possible while keeping the stego-text as natural as possible. We show that this problem is equivalent to maximizing the entropy of a replacement probability distribution of the next token generation, subject to a constraint on the divergence between the new distribution and the original one produced by the LLM. A closed-form solution is provided under either the KL divergence or the total variation constraint. Several important practical issues are also tackled: 1) An often-overlooked tokenization mismatch issue is resolved with a simple prompt selection approach, 2) The combination of the optimized distribution and the vocabulary truncation technique is considered, and 3) The incorporation of the proposed approach with existing (potentially non arithmetic coding based) techniques, e.g., the Discop technique.