Bring the chicken stock to a boil in a small saucepan. Pour it over the cèpes in a small bowl and let stand for 2 hours.
Meanwhile, trim stems from the fresh mushrooms and save stems for another use, or discard. Wipe mushroom caps with a damp paper towel and slice thin.
Melt the butter in a skillet. Add the shallots and sauté gently for 5 minutes without browning.
Meanwhile, drain the cèpes, reserving the liquid, and chop them fine. Add cèpes and sliced fresh mushrooms to the skillet, season with salt and pepper, and sauté over medium heat, stirring occasionally, for 10 minutes.
Preheat oven to 325°F.
Add reserved soaking liquid, the Port and heavy cream to the skillet with the mushrooms and simmer for another 5 minutes, or until slightly thickened.
Spoon mushroom mixture into a shallow baking dish. Arrange chicken breast halves in a single layer on top of the mushrooms. Season with salt and pepper to taste and cover the baking dish tightly with a piece of foil.
Set dish on the middle level of the oven and bake for 20 minutes, or until chicken breasts are done. Sprinkle with chopped parsley and serve immediately.