Existing methods for converting natural language into visualizations operate as black boxes, making it difficult for users to understand the design rationale and improve the results. In this paper, we address this issue by integrating Chain-of-Thought (CoT) inference into the NL2VIS pipeline. First, we design a comprehensive CoT inference process for NL2VIS and develop an automated pipeline that adds structured inference steps to existing datasets. Second, we introduce the nvBench-CoT dataset, which details the step-by-step inference process from ambiguous natural language descriptions to final visualizations, to help improve model performance. Finally, we develop DeepVIS, an interactive visual interface that allows users to review inference steps, identify errors, and adjust visualization results to improve them. Through quantitative benchmark evaluations, two use cases, and user studies, we demonstrate that the CoT framework enhances the quality of NL2VIS and provides users with insightful inference steps.