In a large saucepan melt the butter and add the oil. Cook and stir the onion over a medium heat until soft then add the orange juice, stock and tarragon. Cover and simmer for 15 minutes on a low heat.
Blend the cornflour with 2 tablespoons cold water and stir into the orange tarragon sauce, cook and stir until thickened. Taste and adjust seasoning if desired. Add the chicken breasts and the soured cream and heat through.