Driven by ChatGPT's popularity, generative conversational artificial intelligence (GCAI) has captured global interest. Despite its widespread adoption, the competencies of GCAI and their influence on users' intention to use it remain underexplored. This study examines the effect of GCAI competencies on users' intention to use GCAI. Using a mixed-methods approach, we analyze social media comments and identify four key GCAI competencies. Based on media naturalness theory, trust literature, and the stimulus-organism-response model, we propose and test a research model via a survey. Our results show that accuracy of response, self-learning, and natural language interaction enhance users' intention to use GCAI and trust in it, while human-like empathy influences trust but not intention. Trust fully mediates the relationship between human-like empathy and intention, and partially mediates the relationship between the other three competencies and intention. This study fills a gap in understanding GCAI's appeal and offers guidance for developers and marketers.