Until now, online platforms are by and large exempt from liability for unlawful third party content, and they exempt any liability for such content in the standard terms of their contracts with users. The new Digital Services Act introduces new duties of online platforms, some of which relate to their dealings with information provided by third parties to consumers and with illegal content. However, it is designed as a public law instrument. The article explores whether those new duties, or rather their breach, can nevertheless trigger civil liability of online platforms towards victims of unlawful third party content, where harm could have been avoided if the online platform had complied with its duties, and it presents examples where this seems possible.