Annotations are essential to communicative visualization, helping explain data, emphasize key findings, and guide attention. While multimodal large language models (MLLMs) offer new opportunities for automatic chart annotation authoring, their capabilities in this task remain underexplored. To address this gap, we introduce ChartAnno, a comprehensive benchmark for evaluating MLLMs on chart annotation generation. ChartAnno contains 1,200 real-world charts with paired annotated and unannotated executable code, along with 3,600 annotation instructions spanning three levels of specificity. We also develop a multidimensional evaluation framework combining rule-based and LLM-judged metrics to assess execution, structural compliance, semantic consistency, and design effectiveness. We evaluate 10 representative MLLMs under two primary chart input settings: (1) chart code alone and (2) both code and chart image. Results reveal that proprietary models lead overall, though open-source models narrow the gap. While higher instruction specificity improves annotation quality, inferring abstract communicative intent remains difficult across all models. Providing chart images yields marginal benefit when code is available. We also examine the effect of chart code through an image-only ablation and analyze the effects of multiple task complexity indicators and instruction-level transitions. Further analyses characterize common failure modes and validate the reliability of the LLM-based judge. Experiments with D3 and SVG demonstrate the generalizability of ChartAnno beyond its primary Python setting.

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