Active time: 50 minutes
Heat grill to medium. Slice each chicken breast in half horizontally into 2 evenly thick halves.
Whisk together garlic, lime juice, and olive oil in a large bowl. Season to taste with salt and pepper. Add chicken and turn pieces to thoroughly coat. Let marinate 10 minutes, and up to 30 minutes, at room temperature.
Meanwhile, make the peanut sauce. In a food processor or blender combine all ingredients and process until smooth, adding more water if needed to thin.
Grill chicken until browned and cooked through, 2 to 3 minutes per side.
Transfer chicken to a platter. Spoon peanut sauce over the chicken and sprinkle with cilantro, if desired. Offer remaining peanut sauce on the side.
DO AHEAD: Peanut sauce can be made 3 days ahead.