Keeping up to date on emerging entities that appear every day is indispensable for various applications, such as social-trend analysis and marketing research. Previous studies have attempted to detect unseen entities that are not registered in a particular knowledge base as emerging entities and consequently find non-emerging entities since the absence of entities in knowledge bases does not guarantee their emergence. We therefore introduce a novel task of discovering truly emerging entities when they have just been introduced to the public through microblogs and propose an effective method based on time-sensitive distant supervision, which exploits distinctive early-stage contexts of emerging entities. Experimental results with a large-scale Twitter archive show that the proposed method achieves 83.2% precision of the top 500 discovered emerging entities, which outperforms baselines based on unseen entity recognition with burst detection. Besides notable emerging entities, our method can discover massive long-tail and homographic emerging entities. An evaluation of relative recall shows that the method detects 80.4% emerging entities newly registered in Wikipedia; 92.8% of them are discovered earlier than their registration in Wikipedia, and the average lead-time is more than one year (578 days).