In processor, puree raspberries. Force through strainer over bowl to remove seeds. Stir in seedless raspberry preserves; reserve 2 tablespoons. Cook rice in 3 cups chicken broth, following package directions. Add fresh mint to rice.
Meanwhile, season chicken breast halves with salt and pepper. Grill, smooth side down, over medium-high heat, 4 to 5 minutes. Flip over. Brush with 2 tablespoons raspberry puree; grill 5 minutes (internal temperature 170 degrees F).
In skillet, sauté chopped red onion in oil to soften, 6 minutes. Add remaining puree, 4.5-ounce can diced green chiles, 1/4 teaspoon salt and pinch cayenne; cook 5 minutes. Serve chicken with sauce and rice. Makes 6 servings.