Cut the orange (including peel) into 16 chunks, discarding any seeds. Working in batches in a food processor or blender, add orange chunks, cranberries, and sugar.
Pulse to chop finely and evenly, scraping down the sides of the bowl as needed. Transfer to a container, cover, and refrigerate at least 8 hours or overnight. Bring to room temperature and stir well before serving.
Orange: Or substitute a blood orange, a tangerine, or a couple of clementines.
Yield: This recipe makes 2 cups (1 pint) or 8 (1/4-cup) servings.
Make ahead: Make this relish up to 3 days in advance (store covered in the refrigerator). The flavor improves the longer it sits.
Freezer: Freeze for up to 3 months. Thaw overnight in the refrigerator.
Ginger: 1-2 tablespoons fresh ginger may be added to the food processor with the cranberries.