Cover the bottom of a springform pan with parchment paper or line a round cake pan with plastic wrap (drape the wrap over the sides so that you can lift the pie from the pan when it's ready).
Let the green sherbet soften at room temperature for 10 minutes, then spread 3 cups around the perimeter of the pan. Cover it with plastic and freeze it for 45 minutes.
Add a ring using 2 cups softened white sorbet and refreeze.
Stir 1/3 cup mini chocolate chips into 3 cups softened red sorbet, then fill the center with the mixture.
Freeze the entire dish until firm, about 6 hours. Slice the pie into wedges with a hot knife and serve.