Abstract: In this paper, we present COCI, the OpenCitations Index of Crossref open DOI-to-DOI citations (http://opencitations.net/index/coci). COCI is the first open citation index created by OpenCitations, in which we have applied the concept of citations as first-class data entities, and it contains more than 445 million DOI-to-DOI citation links derived from the data available in Crossref. These citations are described using the resource description framework by means of the newly extended version of the OpenCitations Data Model (OCDM). We introduce the workflow we have developed for creating these data, and also show the additional services that facilitate the access to and querying of these data via different access points: a SPARQL endpoint, a REST API, bulk downloads, Web interfaces, and direct access to the citations via HTTP content negotiation. Finally, we present statistics regarding the use of COCI citation data, and we introduce several projects that have already started to use COCI data for different purposes.