I tried another place for chicken parm sandwiches. Pizza Pino on California at Polk (they have another location on Lombard at Fillmore). I had their chicken parm sandwich and I'd say it was better than Gambino's. It was just a hint toastier with a good amount of cheese.
That being said I was dissappointed to find out that like Gambino's it is just sliced chicken in marinara sauce with mozzerella cheese and NOT breaded. Time to do more searching for the elusive breaded chicken parm sandwich.
Link for previous discussion below.