The rise of generative AI (GenAI) systems trained on content harvested by web-scraping bots threatens the economic viability of the open web. Current legal challenges, often focused on copyright law, fail because the fair use defense allows for uncompensated exploitation. This chapter proposes a new legal framework: reconceptualizing a website – specifically its domain name and underlying architecture – as personal property with a strong right to exclude. This shifts the focus from the content to the container. By arguing that GenAI scraping impairs a website’s value (traffic, ad revenue, subscriber potential) as an economic asset, this approach revitalizes the common law tort of trespass to chattels (Restatement (Second) of Torts § 218). This strategy would empower website owners to enforce exclusionary rights and compel AI companies to negotiate for licenses, ultimately fostering a more sustainable and equitable digital ecosystem.