Preheat grill to high heat. Brush each side of chicken breasts with the cooking oil and season with salt and pepper. Grill 3 minutes on each side, then turn the heat to medium-low and cover to cook for an additional 5 minutes or until cooked through.
In a saucepan or skillet over medium high heat, add all ingredients and stir to combine. Smash half of the berries with a fork to release the juices. Let the mixture cook down for approximately 2 minutes, stirring constantly. Pour over grilled chicken and serve immediately.