Start by roasting the chestnuts. Preheat the oven to 400°F and cut an "X" on the flat side of each chestnut. Place them on a baking sheet and roast for 15-20 minutes or until the shells start to peel away from the nuts. Let them cool, then remove the shells and chop the nuts coarsely.
1 cup roasted chestnuts
In a small saucepan, combine the water and sugars over medium heat. Stir until the sugar dissolves, then bring the mixture to a boil.
1 cup water, ½ cup white sugar, ½ cup dark brown sugar
Add the chopped chestnuts and vanilla extract to the saucepan and reduce the heat to low. Let the mixture simmer for 10-15 minutes or until it thickens.
1 teaspoon vanilla extract
Remove the saucepan from the heat and let the syrup cool for a few minutes.
Strain the syrup through a fine-mesh sieve to remove any solid pieces of chestnut. Transfer the syrup to an airtight container and store it in the refrigerator for up to two weeks.