In a blender, combine all ingredients except chicken until smooth. Pour marinade into a large resealable plastic bag.
Cut chicken breast halves in half again crosswise and slash each piece diagonally three or four times. Add to marinade, toss well to coat evenly, and chill in bag overnight.
Heat grill to medium (about 400°). Oil cooking grate, using tongs and a wad of oiled paper towels. Remove chicken from marinade and grill, turning as needed, until chicken is opaque and grill marks appear, 8 to 10 minutes.