Modern software package registries like PyPI have become critical infrastructure for software development, but are increasingly exploited by threat actors distributing malicious packages with sophisticated multi-stage attack chains. While Large Language Models (LLMs) offer promising capabilities for automated code analysis, their application to security-critical malware detection faces fundamental challenges, including hallucination and context confusion, which can lead to missed detections or false alarms. We present CHASE (Collaborative Hierarchical Agents for Security Exploration), a high-reliability multi-agent architecture that addresses these limitations through a Plan-and-Execute coordination model, specialized Worker Agents focused on specific analysis aspects, and integration with deterministic security tools for critical operations. Our key insight is that reliability in LLM-based security analysis emerges not from improving individual model capabilities but from architecting systems that compensate for LLM weaknesses while leveraging their semantic understanding strengths. Evaluation on a dataset of 3,000 packages (500 malicious, 2,500 benign) demonstrates that CHASE achieves 98.4% recall with only 0.08% false positive rate, while maintaining a practical median analysis time of 4.5 minutes per package, making it suitable for operational deployment in automated package screening. Furthermore, we conducted a survey with cybersecurity professionals to evaluate the generated analysis reports, identifying their key strengths and areas for improvement. This work provides a blueprint for building reliable AI-powered security tools that can scale with the growing complexity of modern software supply chains. Our project page is available at: https://t0d4.github.io/CHASE-AIware25/