Place the chicken in a gallon-sized ziploc bag. Pour in the pesto, rice vinegar, salt and sugar. Seal the bag and shake it up until the marinade is combined and the chicken is well coated.
Refrigerate for at least 2 hours or up to 12 hours.
Preheat an outdoor grill. Grill the chicken for 5-6 minutes on each side until cooked through (or an instant read thermometer reaches 160 degrees). Tent the chicken with foil and let rest 5-10 minutes before slicing and serving.
Alternately, the chicken can be broiled or cooked on an indoor grill pan or skillet.