Large Language Models (LLMs) exhibit remarkable generative capabilities, enabling the generation of valuable information. Despite these advancements, previous research found that LLMs sometimes struggle with adhering to specific constraints, such as being in a specific place or at a specific time, and at times even overlook them, which leads to responses that are either too generic or not fully satisfactory. Existing approaches attempted to address this issue by decomposing and rewriting input instructions or reflecting on prior failings, yet they fall short in adequately emphasizing specific constraints and unlocking the underlying knowledge, such as programming within the context of software development. In response, this paper proposes a simple yet effective method called Chain-of-Specificity (CoS). Specifically, CoS emphasizes the specific constraints in the input instructions, unlocks knowledge within LLMs, and refines responses. Experiments conducted on publicly available and self-built complex datasets demonstrate that CoS outperforms existing methods in enhancing generated content, especially in terms of specificity. Additionally, as the number of specific constraints increases, other baselines falter, while CoS still performs well. Moreover, we show that distilling responses generated by CoS effectively enhances the ability of smaller models to follow constrained instructions.