1Whisk together 3 tablespoons olive oil and garlic and brush mixture on the chicken breasts coating both sides; season with salt and pepper. Cover with plastic wrap and refrigerate until ready to use.
2To make the sauce, add remaining olive oil, lemon juice and zest, capers, and sugar to a small sauce pan and warm over low heat.
3Heat grill (or grill pan if cooking on stovetop) to medium-high.
4Lightly oil the grill grate and place chicken on hot grate. Grill chicken, turning once, until an instant read thermometer registers 165 degrees, about 5-6 minutes per side. Remove from heat and let rest for 5 minutes.
5While chicken is resting, bring sauce mixture to a boil and then spoon over chicken. Serve hot.