In a bowl, combine all the ingredients for the dressing/marinade except for the vinegar.
Place the chicken in a second bowl or other container. Add 3 tbsp. of the marinade, and let marinate 30 to 60 minutes.
In the first bowl, whisk the white wine vinegar into the remaining marinade to create the dressing.
Preheat a grill to medium-high heat.
Place the chicken on the preheated grill discarding any remaining marinade (but don’t throw out the dressing, just the marinade that was in with the chicken).
Cook for 5 to 6 minutes per side, or until no longer pink in the center. Let rest for 5 minutes.
Thinly slice the chicken breasts.
In a bowl, combine all the remaining ingredients, drizzle with the vinaigrette, and toss gently.