Web search is a crucial technology for the digital economy. Dominated by a few gatekeepers focused on commercial success, however, web publishers have to optimize their content for these gatekeepers, resulting in a closed ecosystem of search engines as well as the risk of publishers sacrificing quality. To encourage an open search ecosystem and offer users genuine choice among alternative search engines, we propose the development of an Open Web Index (OWI). We outline six core principles for developing and maintaining an open index, based on open data principles, legal compliance, and collaborative technology development. The combination of an open index with what we call declarative search engines will facilitate the development of vertical search engines and innovative web data products (including, e.g., large language models), enabling a fair and open information space. This framework underpins the EU-funded project OpenWebSearch.EU, marking the first step towards realizing an Open Web Index.