Look for evenly sized peppers that have good firm bottoms for standing upright.
Remove the tops from the peppers and reserve. Remove the seeds.
Place the peppers in boiling water (without the tops) in a covered saucepan for 4 to 5 minutes until tender, but still keeping their shape. Transfer the pepper bottoms to a roasting pan.
Mince the chicken with a knife and place in a large mixing bowl with the basil and the olive oil. Toss gently.
In a medium saucepan, bring the broth, tomato juice, oregano and rice to a boil; then turn down to a simmer, cooking until the rice is soft (about 6 minutes). Stir in the chopped chicken. Remove from the heat and let stand just a few minutes, covered until the rice absorbs any remaining liquid.
Stir in the chopped tomatoes.
Combine cheeses in a small bowl.
Stir in half the cheese mixture into the chicken filling and evenly divide among the peppers. Top with the remaining cheese.
Place stuffed peppers on a sheet pan and place under the broiler until the cheese melts and turns a light golden color.
Place peppers on a serving platter with their tops leaning against each one and a basil sprig for garnish on each one. Or, you can prop the top on an angle adhering it to the pepper with a toothpick.