This paper presents the first large-scale analysis of public-facing chatbots on Character$.$AI, a rapidly growing social media platform where users create and interact with chatbots. Character$.$AI is distinctive in that it merges generative AI with user-generated content, enabling users to build bots for others to engage with. It is also popular, with over 20 million monthly active users, and impactful, with headlines detailing significant issues with youth engagement on the site. Character$.$AI is thus of interest to study both substantively and conceptually. To this end, we present a descriptive overview using a dataset of 2.1 million English-language prompts (or "greetings") from chatbots on the site, created by around 1 million users. Our work explores the prevalence of different fandoms on the site, broader tropes that persist across fandoms, and how dynamics of power intersect with gender within greetings. Overall, our findings illuminate an emerging form of online (para)social interaction at a unique and important intersection between generative AI and user-generated content.