Place the chestnuts in a large pan covering them with water. Bring the water to a boil and cook the chestnuts for 10 minutes. Drain and throw the cooking liquid. Using a clean towel or kitchen cloth, rub the thin skin off the cooked chestnuts.
In a separate pan, boil the 2 1/2 cups water, granulated sugar, and the vanilla stirring constantly. Continue cooking the mixture, stirring occasionally, for 5 additional minutes. Add the chestnuts to the boiling sugar syrup and stir until the whole mixture boils again. Continue cooking the chestnuts, stirring frequently, for 10 minutes. Pour the candied chestnuts, along with the vanilla sugar syrup into a large container, and cover it. Allow the chestnuts to soak for 12 to 18 hours.
Add the chestnuts and syrup to a clean pan and boil them again for 2 minutes.Soak the mixture, loosely covered, for 18 to 24 hours. Repeat the entire process a total of 3 to 4 times, until the sugar syrup has been absorbed by the chestnuts.
Once done preheat an oven to 250F and arrange the candied chestnuts on a baking sheet. Place the baking sheet into the oven and turn off the heat. Allow the chestnuts to dry in the oven for 45 minutes to 1 hour, until they have firmed up and the surfaces of the nuts are dry.