Preheat your grill to medium-high. Place the first 6 ingredients in a small pot. Bring to a simmer and cook and stir until the jam is melted and well incorporated with the other ingredients. Strain the mixture through a fine sieve into a second small pot. Stir in the raspberries and mint; season with salt and pepper.
Cover and reserve sauce on low heat. Brush the chicken with the oil; season with salt and pepper. Grill 4 minutes per side, or until cooked through. Plate the chicken, top with sauce and serve.