Preheat grill to medium-high heat.
Season chicken breasts with salt and pepper.
Grill chicken for 4-5 minutes on each side, or until cooked through. Remove from grill and let rest for a few minutes before slicing.
In a large bowl, combine daikon radish, carrot, cucumber, red onion, cilantro, and mint.
In a small bowl, whisk together lime juice, soy sauce, and sesame oil. Pour over salad ingredients and toss to combine.
Slice grilled chicken and arrange on top of salad. Serve immediately.