Grate the orange peel (the zest) taking care not to grate the white part below the skin. Discard the white part (called the “pith”) and break the orange into sections.
Put the orange zest, orange sections, cranberries and sugar in a food processor and pulse them until the mixture is chunky, but without large pieces of either orange or cranberry.
Refrigerate the mixture for at least 2 hours before serving.