COVID-19 has been a massive disruption in 2020, exacerbated by the spread of misinformation on social media. In this report we ask who is sharing COVID-19 fake news on Twitter, and which URLs are being shared? We show that older people are more likely to share URLs from fake news domains, despite being less likely to believe COVID-19 misinformation. We also show that Republicans are more likely to share fake news than Democrats and Independents. Finally, the fake news domain that has been shared the most in COVID-19 tweets is the Gateway Pundit, which, throughout the COVID-19 pandemic, has received an order of magnitude more shares than even the second most popular fake news domain.