Zest 2 oranges and set zest aside. Cut all oranges in half crosswise and juice enough to make 3 cups.
Heat 3/4 cup orange juice, the sugar, and corn syrup in a large saucepan over medium-high heat until sugar dissolves, 3 to 4 minutes. Remove from heat and stir in zest, remaining juice, and the Campari. Nest pan in a bowl of ice water, stirring occasionally, until mixture is cold, about 20 minutes.
Meanwhile, melt chocolate in a shallow metal bowl set over a saucepan with about 1 in. barely simmering water. Set a sheet of parchment paper flat on a baking sheet. Spread chocolate on top in a 7-in. square. Freeze until firm, at least 20 minutes; keep in freezer.
Freeze juice mixture in an ice cream maker according to manufacturer's instructions, about 25 minutes. Transfer to a metal bowl, cover, and freeze 1 hour. Break up chocolate into pieces about 1/2 by 1 in. Stir sorbet to blend, then fold in chocolate with a flexible spatula until evenly distributed. Freeze until sorbet is firm enough to scoop, at least 3 more hours. Stir well one more time before serving.
Make ahead: Up to 1 week; before serving, let stand at room temperature 15 to 20 minutes to soften.
Recipe is gluten free if made with gluten-free chocolate.