We present PlotChain, a deterministic, generator-based benchmark for evaluating multimodal large language models (MLLMs) on engineering plot reading-recovering quantitative values from classic plots (e.g., Bode/FFT, step response, stress-strain, pump curves) rather than OCR-only extraction or free-form captioning. PlotChain contains 15 plot families with 450 rendered plots (30 per family), where every item is produced from known parameters and paired with exact ground truth computed directly from the generating process. A central contribution is checkpoint-based diagnostic evaluation: in addition to final targets, each item includes intermediate 'cp_' fields that isolate sub-skills (e.g., reading cutoff frequency or peak magnitude) and enable failure localization within a plot family. We evaluate four state-of-the-art MLLMs under a standardized, deterministic protocol (temperature = 0 and a strict JSON-only numeric output schema) and score predictions using per-field tolerances designed to reflect human plot-reading precision. Under the 'plotread' tolerance policy, the top models achieve 80.42% (Gemini 2.5 Pro), 79.84% (GPT-4.1), and 78.21% (Claude Sonnet 4.5) overall field-level pass rates, while GPT-4o trails at 61.59%. Despite strong performance on many families, frequency-domain tasks remain brittle: bandpass response stays low (<= 23%), and FFT spectrum remains challenging. We release the generator, dataset, raw model outputs, scoring code, and manifests with checksums to support fully reproducible runs and retrospective rescoring under alternative tolerance policies.