We present ELQ, a fast end-to-end entity linking model for questions, which uses a biencoder to jointly perform mention detection and linking in one pass. Evaluated on WebQSP and GraphQuestions with extended annotations that cover multiple entities per question, ELQ outperforms the previous state of the art by a large margin of +12.7% and +19.6% F1, respectively. With a very fast inference time (1.57 examples/s on a single CPU), ELQ can be useful for downstream question answering systems. In a proof-of-concept experiment, we demonstrate that using ELQ significantly improves the downstream QA performance of GraphRetriever (arXiv:1911.03868). Code and data available at https://github.com/facebookresearch/BLINK/tree/master/elq