Directed greybox fuzzing (DGF) aims to efficiently trigger bugs at specific target locations by prioritizing seeds whose execution paths are more likely to mutate into triggering target bugs. However, existing DGF approaches suffer from imprecise probability calculations due to their reliance on complex distance metrics derived from static analysis. The over-approximations inherent in static analysis cause a large number of irrelevant execution paths to be mistakenly considered to potentially mutate into triggering target bugs, significantly reducing fuzzing efficiency. We propose to replace static analysis-based distance metrics with precise call stack representations. Call stacks represent precise control flows, thereby avoiding false information in static analysis. We leverage large language models (LLMs) to predict vulnerability-triggering call stacks for guiding seed prioritization. Our approach constructs call graphs through static analysis to identify methods that can potentially reach target locations, then utilizes LLMs to predict the most likely call stack sequence that triggers the vulnerability. Seeds whose execution paths have higher overlap with the predicted call stack are prioritized for mutation. This is the first work to integrate LLMs into the core seed prioritization mechanism of DGF. We implement our approach and evaluate it against several state-of-the-art fuzzers. On a suite of real-world programs, our approach triggers vulnerabilities $1.86\times$ to $3.09\times$ faster compared to baselines. In addition, our approach identifies 10 new vulnerabilities and 2 incomplete fixes in the latest versions of programs used in our controlled experiments through directed patch testing, with 10 assigned CVE IDs.