The outbreak of the COVID-19 pandemic has changed our lives in unprecedented ways. In the face of the projected catastrophic consequences, most countries have enacted social distancing measures in an attempt to limit the spread of the virus. Under these conditions, the Web has become an indispensable medium for information acquisition, communication, and entertainment. At the same time, unfortunately, the Web is being exploited for the dissemination of potentially harmful and disturbing content, such as the spread of conspiracy theories and hateful speech towards specific ethnic groups, in particular towards Chinese people and people of Asian descent since COVID-19 is believed to have originated from China. In this paper, we make a first attempt to study the emergence of Sinophobic behavior on the Web during the outbreak of the COVID-19 pandemic. We collect two large datasets from Twitter and 4chan's Politically Incorrect board (/pol/) over a time period of approximately five months and analyze them to investigate whether there is a rise or important differences with regard to the dissemination of Sinophobic content. We find that COVID-19 indeed drives the rise of Sinophobia on the Web and that the dissemination of Sinophobic content is a cross-platform phenomenon: it exists on fringe Web communities like /pol/, and to a lesser extent on mainstream ones like Twitter. Using word embeddings over time, we characterize the evolution of Sinophobic slurs on both Twitter and /pol/. Finally, we find interesting differences in the context in which words related to Chinese people are used on the Web before and after the COVID-19 outbreak: on Twitter we observe a shift towards blaming China for the situation, while on /pol/ we find a shift towards using more (and new) Sinophobic slurs.