Every year, millions of dollars are invested and spent on works covered by copyright. However, in the platform economy, where most content is currently stored and viewed, copyright holders face infringements of their rights at an ever-increasing scale. While Section 230 of the Communications Decency Act serves a useful speech-protecting function, unless the United States is willing to forego copyright law and the economic interests that it protects, some effort is needed to develop an efficient mechanism of copyright enforcement for platforms. In this paper, we pull together copyright law, the law of platform liability, and the economics of enforcement to explore models of no liability, notice and takedown, strict liability, and negligence. We discuss how platform liability can encourage the creation of creative work, but may also lead to over-blocking and chilling effects. Using a formal model, we consider what mechanisms of copyright enforcement can maintain the speech protections of Section 230 while incentivizing authors to create new works.