The increasing frequency and sophistication of cybersecurity vulnerabilities in software systems underscore the urgent need for robust and effective methods of vulnerability assessment. However, existing approaches often rely on highly technical and abstract frameworks, which hinders understanding and increases the likelihood of exploitation, resulting in severe cyberattacks. Given the growing adoption of Large Language Models (LLMs) across diverse domains, this paper explores their potential application in cybersecurity, specifically for enhancing the assessment of software vulnerabilities. We propose ChatNVD, an LLM-based cybersecurity vulnerability assessment tool leveraging the National Vulnerability Database (NVD) to provide context-rich insights and streamline vulnerability analysis for cybersecurity professionals, developers, and non-technical users. We develop three variants of ChatNVD, utilizing three prominent LLMs: GPT-4o mini by OpenAI, Llama 3 by Meta, and Gemini 1.5 Pro by Google. To evaluate their efficacy, we conduct a comparative analysis of these models using a comprehensive questionnaire comprising common security vulnerability questions, assessing their accuracy in identifying and analyzing software vulnerabilities. This study provides valuable insights into the potential of LLMs to address critical challenges in understanding and mitigation of software vulnerabilities.