Understanding how complex societal behaviors emerge from individual cognition and interactions requires both high-fidelity modeling of human behavior and large-scale simulations. Traditional agent-based models (ABMs) have been employed to study these dynamics for decades, but are constrained by simplified agent behaviors that fail to capture human complexity. Recent advances in large language models (LLMs) offer new opportunities by enabling agents to exhibit sophisticated social behaviors that go beyond rule-based logic, yet face significant scaling challenges. Here we present Light Society, an agent-based simulation framework that advances both fronts, efficiently modeling human-like societies at planetary scale powered by LLMs. Light Society formalizes social processes as structured transitions of agent and environment states, governed by a set of LLM-powered simulation operations, and executed through an event queue. This modular design supports both independent and joint component optimization, supporting efficient simulation of societies with over one billion agents. Large-scale simulations of trust games and opinion propagation--spanning up to one billion agents--demonstrate Light Society's high fidelity and efficiency in modeling social trust and information diffusion, while revealing scaling laws whereby larger simulations yield more stable and realistic emergent behaviors.