Radical right influencers routinely use social media to spread highly divisive, disruptive and anti-democratic messages. Assessing and countering the challenge that such content poses is crucial for ensuring that online spaces remain open, safe and accessible. Previous work has paid little attention to understanding factors associated with radical right content that goes viral. We investigate this issue with a new dataset (ROT) which provides insight into the content, engagement and followership of a set of 35 radical right influencers. It includes over 50,000 original entries and over 40 million retweets, quotes, replies and mentions. We use a multilevel model to measure engagement with tweets, which are nested in each influencer. We show that it is crucial to account for the influencer-level structure, and find evidence of the importance of both influencer- and content-level factors, including the number of followers each influencer has, the type of content (original posts, quotes and replies), the length and toxicity of content, and whether influencers request retweets. We make ROT available for other researchers to use.