For the chicken: In a baking dish, mix the fish sauce, lime juice sugar, garlic, jalapeno and salt. Add the chicken breasts to the dish, cover, and refrigerate at least 1 hour. Longer is better!
For the pickled vegetables: Stir the hot tap water and sugar in a medium bowl, until the sugar dissolves. Add the vinegar, salt, crushed red pepper, sliced carrots and radishes. Cover and refrigerate for at least 30 minutes.
Heat the grill to medium. Grill the chicken breasts for 5 minutes per side. Remove from heat and cover the chicken with foil to rest for 5 minutes. Open the sub rolls and grill the insides for about 1-3 minute—until toasted.
Drain the pickled veggies. Slice the chicken into thin pieces.
Spread mayo over in the sub rolls. Layer the cucumbers, chicken, pickled veggies, cilantro leaves and jalapeños in the rolls. Serve immediately!