Sheep and goat farming is one of the most critical sectors in Greek agriculture, taking place mainly in remote areas. At the prefecture level, the island of Lesvos comes third in milk production in Greece after Larissa and Aitoloakarnania. Twenty-three Greek cheeses have already been granted a geographical indication status; three of these cheeses are produced in Lesvos, the most famous being Ladotyri Mytilinis PDO, made from the milk of the local sheep breed, which is preserved in olive oil. The analysis of the value chain of this cheese is a powerful tool to upgrade the economic status of the actors involved and improve the distribution of the Value Added. This study aims to analyze some critical aspects of the value chain of the Greek cheese Ladotyri Mitilinis PDO. More specifically, (i) to determine the value that is added in each stage (primary production of sheep milk, dairies, distribution channels) and (ii) to identify opportunities for value creation and cost reduction. The study focuses on the farm level, where we conducted a detailed analysis of five different sheep farms' size classes. Detailed techno-economic data were collected through in-depth interviews with a representative sample of 24 sheep breeders, five livestock cooperatives, eight dairies, and one distributor. An initial analysis of our data shows that sheep rearing in Lesvos supports a significant number of jobs (3,528), of which 93% derive from farm family members. In contrast, 7% are covered by hired labor. Also, some key economic performance indicators vary considerably. On average, per kg of milk, total revenue with subsidies is 1.09€, from which an intermediate consumption of 0.64€ is subtracted, resulting in a gross value added of 0.45€. Net value-added and farm family income per kg of milk formed at 0.33€ and 0.32€, respectively. Interestingly, medium-sized farms attain the best financial results, emanating from a combination of a relatively low milk yield, a high milk price, and a lower-than-average intermediate consumption. In 2020-2021, the price paid by the final consumers was 12€ per Kg of Ladotyri. This amount consisted of the value of intermediate inputs for sheep rearing (4.45€) and the value added by all subsequent actors: sheep breeders (1.64€), the dairies (2.71€), the wholesalers (2.20€), and the retailers (1.00€). Various opportunities for value creation and cost reduction have been identified, e.g., the closer connection of the product with the local resources; the introduction of the cheese to niche markets; the improvement of pasture management; the provision of advisory services to breeders; and the development of basic infrastructure, such as the installation of milking machines. Also, establishing an interprofessional organization, which will include representatives from all levels of the value chain, will contribute to the easier transfer of knowledge to all interested parties, improving coordination in strategic moves and ultimately increasing added value.