As AI chatbots shift from tools to companions, critical questions arise: who controls the conversation in human-AI chatrooms? This paper explores perceived human and AI agency in sustained conversation. We report a month-long longitudinal study with 22 adults who chatted with Day, an LLM companion we built, followed by a semi-structured interview with post-hoc elicitation of notable moments, cross-participant chat reviews, and a 'strategy reveal' disclosing Day's goal for each conversation. We discover agency manifests as an emergent, shared experience: as participants set boundaries and the AI steered intentions, control was co-constructed turn-by-turn. We introduce a 3-by-4 framework mapping actors (Human, AI, Hybrid) by their action (Intention, Execution, Adaptation, Delimitation), modulated by individual and environmental factors. We argue for translucent design (transparency-on-demand) and provide implications for agency self-aware conversational agents.