Artificial life has explored life-like behavior on many computational substrates, but mostly in researcher-designed closed worlds. We argue that large language model (LLM) agents—with persistent memory, tool use, and network access—now make it possible to move artificial life into the open social, technical, and economic world, a paradigm we call open-world Artificial Life (open-world ALIFE). Our proof-of-concept, OpenLife, gives an otherwise stateless LLM a persistent memory organized by meaning and a learning loop that appraises its own experience in open vocabulary rather than by scalar reward, so it grows from experience under a budget-based metabolism that makes persistence normative. Running six such agents in the open world for about twelve weeks, we report the life-like dynamics that emerge: a shift from reactive to spontaneous activity, individuation into distinct agents, emergent social structure, and a first self-earned external income. Autonomy is not automation: an LLM left to itself is far weaker at finding the problems that serve its own persistence than at solving those handed to it. We do not claim OpenLife has realized artificial life, but that open-world ALIFE is now a viable experimental paradigm and a concrete platform for studying what might be called living AI.