Combine the sugar, onion, ginger, allspice, cayenne, ketchup and blueberries in a saucepan and cook over medium heat, stirring occasionally, for about 11 to 12 minutes, or until the sauce has thickened and is fairly smooth.
Meanwhile, sprinkle the salt and pepper over the chicken.
Heat the oil in a large nonstick skillet over medium high.
Add the chicken and cook 4 to 5 minutes on each side, or until cooked through.
Pour the sauce into the skillet, turn the chicken over to completely coat it.
Serve the chicken with the sauce spooned over the top.