Marinate the chicken in a few glugs of balsamic vinegar and about 2 grated garlic cloves, salt and pepper, for about an hour prior to cooking.
Cook pasta according to instructions on box. Run under cool water when done, toss with some olive oil and set aside.
Over a hot grill, place peppers with the skins on and red onion, peeled and halved, and chicken. Char onion on all sides and the peppers until black. Remove peppers and place in a brown paper bag for at least 15 minutes to steam and cool. Remove onion once cooked through, slightly charred, but still intact, slice and add to pasta. Once peppers are cooled enough to handle, peel off skins and slice into strips. Add to pasta.
Once chicken is cooked all the way through, remove, slice and add to pasta as well.
To make the dressing, add all ingredients to a jar and shaking until emulsified.
Pour dressing over pasta and all other ingredients, add ample amounts of parmesan and fresh basil, toss well and enjoy.