Although exports of agricultural products contribute to the economic growth of Greece, the export balance remains in deficit. It is therefore uncertain as to whether the Greek food supply properly responds to current global challenges. In this paper we adopt an approach of an integrated international food supply chain and explore the capacity of the Greek food supply chain. Based on a literature review and in-depth interviews with business executives and staff of export certification and inspection bodies we conduct a SWOT analysis. The objective is to generate knowledge on how the Greek food supply chain could become extrovert, and provide recommendations for all members of the supply chain and public authorities. The findings indicate that the most crucial factors that negatively impact export capacity and discourage export initiatives are dispersed beyond the export firm level, and can be categorized in two groups. The first group is connected with the main structural characteristics of the primary production, such as the characteristics of farms and farm owners, barriers and uncertainties caused by natural environment of production, the perishability of the products and the lack of effective collective efforts. The second group is connected with the public authorities and services. These factors include the signing of bilateral phytosanitary contracts with non-EU countries, the bureaucracy in operations of the public services, the registration of exporters where it is needed, the organisation or/and support of the provision of export related information, the insufficient provision of vocational training and agricultural research which is necessary at all supply stages and steps, from the farm business level until the consumption.