Directed greybox fuzzing (DGF) aims to efficiently trigger bugs at specific target locations by prioritizing seeds whose execution paths are more likely to reach the targets. However, existing DGF approaches suffer from imprecise potential estimation due to their reliance on static-analysis-based distance metrics. The over-approximation inherent in static analysis causes many seeds with execution paths irrelevant to vulnerability triggering to be mistakenly prioritized, significantly reducing fuzzing efficiency. To address this issue, we propose trace-guided directed greybox fuzzing (TDGF). TDGF replaces static-analysis-based distance metrics with vulnerability-oriented execution information (referred to as guidance traces) to steer directed fuzzing: seeds whose execution paths overlap more with the guidance traces are scheduled earlier for mutation. We empirically study two representative types of guidance traces: the control-flow trace and the call-stack trace of vulnerability-triggering executions. We find that the fine-grained control-flow traces offer nearly the same guidance capability as the coarse-grained call-stack traces, while call-stack traces are also easier for large language models (LLMs) to predict. Based on this insight, we further propose a framework that leverages LLMs to predict the call stack at vulnerability-triggering time and uses it to guide DGF. We implement our approach and evaluate it against several state-of-the-art fuzzers with experiments totaling 58.4 CPU-years. On a suite of real-world programs, our approach triggers vulnerabilities 2.13$\times$ to 3.14$\times$ faster than the baselines. Moreover, through directed patch testing on the latest program versions used in our controlled experiments, our approach discovers 10 new vulnerabilities and 2 incomplete fixes, with 10 assigned CVE IDs.