Step 1Heat a grill over medium-high heat. Place the chicken in a medium bowl and rub all over with the olive oil and garlic. Season each piece with one-fourth teaspoon salt and a couple of grinds of black pepper.
Step 2Place the chicken on the grill and cook until the meat is opaque and firm and a thermometer inserted into the center reads 165 degrees. Remove the chicken to a plate, squeeze a little juice from the halved lime over the chicken and allow to cool to room temperature, covered loosely.
Step 3In a large bowl, toss together the nappa cabbage, daikon, carrot, cucumber, green onion, cilantro and radish sprouts. Cut the cooled chicken into a half-inch dice and toss with the salad.
Step 4In a small bowl, combine the lime juice, fish sauce, sugar and a good grind of fresh black pepper. Drizzle the dressing over the salad and toss to coat evenly. Serve immediately.