In a large heatproof liquid-measuring cup, microwave 2 cups plus 2 tablespoons of water until hot but not yet boiling. Stir in the sugar and salt until completely dissolved.
In a 1-gallon heavy-duty, resealable plastic freezer bag, add the chestnuts, vodka, and sugar-water mixture. Seal tightly, then place the bag inside a second bag. Squeeze out as much air as possible before sealing the second bag tightly as well.
Heat a large pot of water over medium. When the water reaches 185°F, regulate the heat to maintain a steady temperature. Using 2–3 large metal binder clips, attach the plastic bags to the side of the pot, ensuring that the liquid inside the bags is completely submerged without allowing the bags to touch the bottom of the pot. Cook for 2 hours, checking the temperature every 5–10 minutes. (Most plastic freezer bags begin to melt at around 195°F, so keep the water temperature between 185°–190°F at all times.)
Turn off the heat and let the mixture rest in the hot water bath until it is cool enough to handle. Using tongs, transfer the bags to a large heatproof bowl, then open the bags and pour their contents into the bowl. Set a fine-mesh strainer over the liquid-measuring cup and strain the mixture, discarding the chestnuts. Let the liquid cool to room temperature, then line the strainer with a coffee filter or 2 layers of cheesecloth and strain the liquid once more into a glass bottle or jar. The liqueur will keep for up to 1 year at room temperature.