Place chickens, vegetables, garlic, and herbs in a pan, cover with water, bring to boil, and simmer for 1.5–2 hours.
Strain the stock through a sieve and reserve 700ml for the soup recipe.
Extract the small chicken 'oyster' meat pieces from the thighs and reserve for garnish.
Melt butter with oil in a saucepan and sweat onions and leeks for 5 minutes without browning.
Add potatoes and bouquet garni, cook for 2 minutes, then add the hot stock and boil until potatoes soften.
Remove the bouquet garni, blend the soup until smooth, and chill thoroughly in the refrigerator.
Remove rock oysters from shells, poach briefly in fish stock, and allow to cool.
Divide poached oysters and chicken 'oysters' into bowls, pour over the cold soup, and garnish with chives.