Jailbreak attacks pose a serious threat to Large Language Models (LLMs) by bypassing their safety mechanisms. A truly advanced jailbreak is defined not only by its effectiveness but, more critically, by its stealthiness. However, existing methods face a fundamental trade-off between semantic stealth (hiding malicious intent) and linguistic stealth (appearing natural), leaving them vulnerable to detection. To resolve this trade-off, we propose StegoAttack, a framework that leverages steganography. The core insight is to embed a harmful query within a benign, semantically coherent paragraph. This design provides semantic stealth by concealing the existence of malicious content and ensures linguistic stealth by maintaining the natural fluency of the cover paragraph. We evaluate StegoAttack on four state-of-the-art, safety-aligned LLMs, including GPT-5 and Gemini-3, and benchmark it against eight leading jailbreak methods. Our results show that StegoAttack achieves an average attack success rate (ASR) of 95.50%, outperforming existing baselines across all four models. Critically, its ASR drops by less than 27.00% under external detectors, while maintaining natural language distribution. This demonstrates that steganography effectively decouples linguistic and semantic stealth, thereby posing a fully concealed yet highly effective security threat. The code is available at https://github.com/GenggengSvan/StegoAttack