European farmers of indigenous local breeds have benefited from European Union economic support in the past and it is forecast to continue being supported in the future. However, it is in the public debate that economic support cannot last forever. Then, for the long-run maintenance of indigenous local breeds to be possible, the derived meat products from these breeds should be demanded by consumers or at least by a group of local consumers. This is the aim of this paper, to study consumers’ demand for indigenous local meat products. In particular, to assess how much consumers are willing to pay for a Spanish lamb meat from an indigenous sheep breed (“Ojinegra de Teruel”). To do that, a non-hypothetical experimental auction with local consumers (those living in a medium-size town around 150 km from the producing area of this meat) was used. Results indicated that consumers were willing to pay, on average, €0.45 (15% of the market price) more for the lamb meat with the “Ojinegra de Teruel” breed claim than for the one without breed indication (as it is now sold in the market). Then, local consumers clearly accept the differentiated meat through the indigenous breed indication. Then, producers in the area could have more opportunities to sell in the local market if they differentiate their meat using the indigenous “Ojinegra de Teruel” claim than using the undifferentiated strategy they are undertaken now.