Non-profits, as well as the media, have hypothesized the existence of a radicalization pipeline on YouTube, claiming that users systematically progress towards more extreme content on the platform. Yet, there is to date no substantial quantitative evidence of this alleged pipeline. To close this gap, we conduct a large-scale audit of user radicalization on YouTube. We analyze 330,925 videos posted on 349 channels, which we broadly classified into four types: Media, the Alt-lite, the Intellectual DarkWeb (I.D.W.), and the Alt-right. According to the aforementioned radicalization hypothesis, channels in the I.D.W. and the Alt-lite serve as gateways to fringe far-right ideology, here represented by Alt-right channels. Processing 72M+ comments, we show that the three channel types indeed increasingly share the same user base; that users consistently migrate from milder to more extreme content; and that a large percentage of users who consume Alt-right content now consumed Alt-lite and I.D.W. content in the past. We also probe YouTube's recommendation algorithm, looking at more than 2M video and channel recommendations between May/July 2019. We find that Alt-lite content is easily reachable from I.D.W. channels, while Alt-right videos are reachable only through channel recommendations. Overall, we paint a comprehensive picture of user radicalization on YouTube.