Large language models (LLMs) are increasingly used in finance and economics, where prompt-based attempts against look-ahead bias implicitly assume that models understand chronology. We test this fundamental question with a series of chronological ordering tasks with increasing complexities over facts the model already knows from pre-training. Our tasks cover (1) chronological ordering, (2) conditional sorting (filter, then order), and (3) anachronism detection. We evaluate GPT-4.1, Claude-3.7 Sonnet, with and without Extended Thinking (ET), and GPT-5 across multiple reasoning-effort settings. Across models, Exact match rate drops sharply as sequences lengthen even while rank correlations stay high as LLMs largely preserve local order but struggle to maintain a single globally consistent timeline. In conditional sorting, most failures stem from the filtering step rather than the ordering step, but GPT-5 and Claude-3.7 Sonnet with Extended Thinking outshine normal models significantly. Lastly, anachronism detection is found to be the easiest task for the LLMs but performance still declines with increasingly overlapping timelines or entities. Overall, our main contribution is showing that allocating explicit reasoning budget helps with chronological ordering with GPT-5 at medium/high reasoning effort achieving flawless ordering at all lengths and perfect conditional sorting (both self-filtered and given-subset), whereas low/minimal effort degrades with longer lists, mirroring earlier models. Our findings delineate limits of current LLMs on chronological tasks, providing insights into task complexity, and demonstrate scenarios in which reasoning helps. These patterns are important for the real-time application of LLMs in finance. We release all code and evaluation templates to support full reproducibility.