As Large Language Models (LLMs) are widely deployed in diverse scenarios, the extent to which they could tacitly spread misinformation emerges as a critical safety concern. Current research primarily evaluates LLMs on explicit false statements, overlooking how misinformation often manifests subtly as unchallenged premises in real-world user interactions. We curated ECHOMIST, the first comprehensive benchmark for implicit misinformation, where the misinformed assumptions are embedded in a user query to LLMs. ECHOMIST is based on rigorous selection criteria and carefully curated data from diverse sources, including real-world human-AI conversations and social media interactions. We also introduce a new evaluation metric to measure whether LLMs can recognize and counter false information rather than amplify users' misconceptions. Through an extensive empirical study on a wide range of LLMs, including GPT-4, Claude, and Llama, we find that current models perform alarmingly poorly on this task, often failing to detect false premises and generating misleading explanations. Our findings underscore the critical need for an increased focus on implicit misinformation in LLM safety research.