The Commission recently proposed a Regulation which aims to lay down uniform rules to prevent the misuse of hosting services for the dissemination of terrorist content online. Its subject matter amounts to an interference with freedom of expression to the extent that it brings within its scope speech protected under the EU Charter of Fundamental Rights and the ECHR. The Proposal has already sparked considerable controversy and triggered debate on its fundamental rights implications as regards freedom of expression but also other fundamental rights. If adopted, it will constitute a remarkable internal market legislation providing for a harmonised restriction of fundamental rights, with the aim to combat terrorism. This paper will investigate the proposed Regulation, focusing especially on the fact that, as an internal market instrument, it shifts an important share of the responsibility for addressing the problem of dissemination of terrorist content online to private parties.