Tenderize (or pierce) chicken breasts to make a uniform thickness. If you have 2 large pieces, cut in halves to make 4.
Place chicken in an airtight baggie with Italian dressing, marinating for a minimum of 1 hour, but up to overnight.
Heat the grill to medium-high heat, about 350°F. Spray or oil the grates to reduce sticking.
Cook chicken on each side for 7-8 minutes. Close the lid in between turning to ensure even cooking. Check to make sure chicken registrars at 160°F.
Remove and allow chicken to rest for 5 minutes, at which point carry over cooking should allow the temperature to come up to 165°F.
Spread chipotle aioli sauce on one side of the sandwich roll. On each roll place a leaf of lettuce, slice of tomato, chicken, 2 slices of bacon, 1 slice of pepper jack cheese, three slices of avocado. Top with other half of roll.
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Chicken sizes should be about the size to fit a large bun. Depending on the the size, this might mean two large butterflied or 4 small pieces. Use your best judgement.