Place the chicken breasts in a large resealable plastic bag. Add the vinegar, olive oil, and crushed garlic. Seal and refrigerate for at least 30 minutes to marinate. Once marinated, sauté the chicken in a pan with a small amount of olive oil over medium heat until fully cooked. Allow to cool slightly, then chop or shred into small pieces.

In a large pot of salted boiling water, cook the manicotti shells until al dente, following the package instructions. Drain carefully and set aside, taking care not to tear the pasta.

In a medium saucepan, melt the butter over medium-high heat. Add the heavy cream, salt, nutmeg, and black pepper, stirring frequently. Allow the mixture to simmer gently until it thickens slightly. Reduce heat to low and incorporate the Parmesan cheese, stirring until fully melted and smooth. Remove from heat and set aside.

In a large mixing bowl, combine the ricotta cheese, egg, oregano, marjoram, and basil. Stir in the cooked chicken until evenly distributed.

Preheat the oven to 350°F (175°C). Spread half of the prepared Alfredo sauce across the bottom of a 9x13-inch baking dish. Using a spoon or piping bag, gently fill each cooked manicotti shell with the chicken and ricotta mixture. Arrange the stuffed shells in the baking dish over the sauce.

Pour the remaining Alfredo sauce over the arranged shells. Sprinkle the shredded mozzarella cheese evenly on top. Cover the dish with aluminum foil and bake for 45 minutes, or until heated through and bubbling. Let the dish stand for 10 minutes before serving.