Cut four pieces of aluminum foil, about 15 inches long each one.
Wash the zucchini and cut it in thin slices.
Chop the chives finely and put them in a small bowl. Squeeze the lemon, adding the juice to the chives. Mix in the heavy cream.
Place each filet on top of its piece of aluminum foil. Salt and pepper the fish lightly. Place the zucchini on top of the fish, evenly dividing it amongst the four pieces. Pour one tablespoon of the cream mixture on top of each filet.
Wrap up each filet in its aluminum foil. You can roll the top edges to make sure everything is secure, but be careful not to tear the aluminum foil.
Place the four packages in an oven proof dish and place the dish in the oven. Cook for 20 minutes.