Heat grill to medium. Meanwhile cut 4 pieces of foil 18x12" and set aside.
Cut potatoes in half for large ones or leave the small ones whole and place a quarter of them on each piece of foil.
Salt each package and drizzle with olive oil.
Slice the chicken crosswise with four slices evenly, careful not to slice all the way through. Place the chicken on top of the potatoes.
Spoon approx. 1 tsp. of pesto into each slit. Place a slice of mozzarella and tomato into each slit.
Season each breast with salt, pepper and Italian seasoning. Drizzle each breast with olive oil.
Bring the two long ends of the foil up to meet and fold down a few times but not tightly. You want to have air to circulate to cook.
Bring up the side inwards so the packs won't leak.
Place directly on grill for 30 min. of until chicken reads 165F and potatoes are tender.
Remove packs from grill and carefully open as they will be hot.
Sprinkle with freshly cut basil if desired.