In a small skillet, heat the oil over medium heat, add the minced garlic and cook slowly, stirring constantly, until softened. Make sure the oil is not too hot. You don't want to brown the garlic and it can get to that point quickly if you're not careful.
Take it off the heat after 5 minutes or so and add the brown sugar and stir it in.
Line a shallow roasting pan with foil and spread oil across the foil. Lay your boneless skinless chicken breasts across it, spread the garlic/oil/brown sugar mix across the chicken. Bake for 15 minutes, or until done.