In a saucepan, combine the grapes, currants, ginger, vinegar, shallot and spices. Cook over medium-high heat, stirring until the grapes wilt and release their juice.
In a small bowl, dissolve the cornstarch in the water. Add to the grapes and continue cooking over medium-low heat for 20 minutes, stirring occasionally, or until the mixture thickens. Season with salt and pepper. Let cool completely. The chutney will keep for 1 week in an airtight container in the refrigerator.