Structured knowledge bases (KBs) are an asset for search engines and other applications but are inevitably incomplete. Language models (LMs) have been proposed for unsupervised knowledge base completion (KBC), yet, their ability to do this at scale and with high accuracy remains an open question. Prior experimental studies mostly fall short because they only evaluate on popular subjects, or sample already existing facts from KBs. In this work, we perform a careful evaluation of GPT’s potential to complete the largest public KB: Wikidata. We find that, despite their size and capabilities, models like GPT-3, ChatGPT and GPT-4 do not achieve fully convincing results on this task. Nonetheless, it provides solid improvements over earlier approaches with smaller LMs. In particular, we show that it is feasible to extend Wikidata by 27M facts at 90% precision.