Little attention has been paid on EArly Rumor Detection (EARD), and EARD performance was evaluated inappropriately on a few datasets where the actual early-stage information is largely missing. To reverse such situation, we construct BEARD, a new Benchmark dataset for EARD, based on claims from fact-checking websites by trying to gather as many early relevant posts as possible. We also propose HEARD, a novel model based on neural Hawkes process for EARD, which can guide a generic rumor detection model to make timely, accurate and stable predictions. Experiments show that HEARD achieves effective EARD performance on two commonly used general rumor detection datasets and our BEARD dataset.