Combine chicken, garlic, 1 tablespoon vinegar, oil and dried basil in a bowl, tossing to coat chicken. Cover with plastic wrap and refrigerate 1 hour.
Meanwhile, combine the remaining 1 tablespoon vinegar, 1 1/2 packages blueberries, shallots, bell pepper, fresh basil, sugar, coriander, 1/8 teaspoon salt and allspice in a bowl; mix well.
Remove chicken from the refrigerator and let stand at room temperature for 5 minutes. Coat a grill pan with cooking spray and heat over medium-high heat. Sprinkle chicken with remaining 1/4 teaspoon salt. Add chicken to grill pan and cook about 5 minutes per side or until a thermometer inserted into the thickest portion registers 165°F. Serve chicken with blueberry relish and remaining blueberries.