Heat grill to medium hot. Season chicken to taste with salt and pepper. With 1 tablespoon oil, lightly coat chicken pieces on all sides. Grill, turning once, until lightly browned and cooked through – about 12-20 minutes, depending on thickness.
Meanwhile, prepare dressing: Stir and press raspberries through a fine sieve to remove juice. Discard seeds. Whisk together raspberry juice, the remaining 2 tablespoons olive oil, the water, parsley, mustard, sugar substitute, and salt and pepper to taste. Finely chop the pecans and add half to raspberry mixture, reserving remaining pecans for topping.
To serve, cut grilled chicken crosswise into 1/2-inch-thick strips. Fan chicken strips on platter; pour dressing over and garnish with remaining chopped pecans and raspberries.
Nutrition information per serving: calories: 343 ; protein: 16g ; carbs: 5g ; saturated fat: 4g ; monounsaturated fat: 19g ; polyunsaturated fat: 5g ; cholesterol: 41mg ; fiber: 2g ; sodium: 43mg.