To roast the nuts, preheat the oven to 350F. Spread the pistachios on an ungreased baking sheet and roast in the oven for 8-10 minutes. Remove from the oven and allow to cool. In a small food processor, process the toasted pistachios until finely chopped, but not powdered. Set aside in a small bowl.
Put about 2 tsp of chevre in the palm of your hand, flatten into a disk and place a grape on top. Fold the cheese over the grape and roll it to completely cover the grape in the cheese. Place it on a baking sheet. Repeat this process until all of the grapes are covered or you run out of cheese.
Set the baking sheet with the grapes in the refrigerator, uncovered, for about 15 minutes to firm them up. Then, roll the cheese-coated grapes in the chopped pistachios until they are coated. Return them to the refrigerator until you are ready to serve them/ They will keep, covered with plastic wrap, for about 4 days