Background/Objectives: Chronic apical periodontitis (CAP) is a persistent periapical inflammatory lesion whose treatment still fails in a substantial fraction of cases, and no molecularly targeted adjunct exists. We aimed to identify druggable hub genes and small-molecule candidates suitable for local intracanal delivery using an integrative computational pipeline. Methods: CAP-associated genes were retrieved from GeneCards and the Open Targets Platform. A protein–protein interaction network, MCODE modules, and three CytoHubba centrality algorithms were used to define hub genes. DrugClip virtual screening and ADMET filtering calibrated for intracanal safety selected candidates, which were assessed by molecular docking with AutoDock Vina, 100 ns molecular dynamics simulations, and per-snapshot binding free-energy analysis. Results: Retrieval yielded 110 non-redundant genes; inflammation was the most enriched process. Eighteen hub genes emerged, with CCL5 and CCR2 among the most central. Screening prioritized MCULE-9834903214 for CCL5 and MCULE-9117306970 for CCR2. The CCR2 complex remained stably engaged, whereas the CCL5 complex was only metastable. Per-snapshot binding free energies over 35–100 ns overlapped in central tendency (−30.5 ± 35.4 vs. −21.6 ± 66.7 kJ·mol⁻¹ for CCR2 and CCL5) but separated by dispersion, with the CCR2 energy trace being nearly twofold tighter. Conclusions: Neither docking affinity nor the mean binding free energy distinguished the leads; the consistency of the binding-energy trace did. MCULE-9117306970 is the priority candidate for experimental validation as a locally delivered anti-inflammatory adjunct against CCR2; MCULE-9834903214 requires redesign to achieve a stable polar anchor. This pipeline yields experimentally testable hypotheses rather than validated therapeutics.