We address the integration of storytelling and Large Language Models (LLMs) to develop engaging and believable Social Chatbots (SCs) in community settings. Motivated by the potential of fictional characters to enhance social interactions, we introduce Storytelling Social Chatbots (SSCs) and the concept of story engineering to transform fictional game characters into "live" social entities within player communities. Our story engineering process includes three steps: (1) Character and story creation, defining the SC's personality and worldview, (2) Presenting Live Stories to the Community, allowing the SC to recount challenges and seek suggestions, and (3) Communication with community members, enabling interaction between the SC and users. We employed the LLM GPT-3 to drive our SSC prototypes, ''David" and ''Catherine," and evaluated their performance in an online gaming community, ''DE (Alias)," on Discord. Our mixed-method analysis, based on questionnaires (N=15) and interviews (N=8) with community members, reveals that storytelling significantly enhances the engagement and believability of SCs in community settings.