Whisk together vinegar, sugar, cloves, and 1 tablespoon of the salt in a medium saucepan. Bring to a boil over medium-high. Continue boiling, stirring occasionally, until sugar and salt dissolve, about 5 minutes. Place onion slices in a medium-size heatproof bowl, and pour hot vinegar mixture over onion. Let cool completely to room temperature, about 30 minutes.

Meanwhile, stir together pepper, 2 tablespoons of the oil, and remaining 1 1/2 teaspoons salt in a small bowl. Brush mixture evenly over chicken breasts. Preheat a gas grill to medium-high (400°F to 450°F). Place chicken on unoiled grates. Grill, uncovered, until a thermometer inserted in thickest portion of meat registers 165°F, 7 to 8 minutes per side. Transfer chicken to a cutting board, and rest 10 minutes. Cut into 3/4-inch slices.

Measure 3 tablespoons onion-pickling liquid into a medium bowl. Add mustard, lemon juice, and remaining 5 tablespoons oil; whisk until smooth. Place salad greens in a large bowl; add mustard mixture, goat cheese, blueberries, and pecans. Toss to coat. Drain remaining pickling liquid from onion; discard liquid and cloves. Add onion to salad; toss to combine. Divide evenly among 4 bowls; top with sliced chicken.