Marinate chicken breasts with the juice of one lemon for 1 to 2 hours prior to grilling. Also mix sauce a few hours early. Cover and refrigerate.
Sauce: Mix 1 clove finely chopped garlic, juice of 1/2 a lemon and mayonnaise.
Tear grilled chicken breasts into bite sized pieces. Squeeze remaining lemon onto meat. Cut pita bread in half. Fill with chicken and top with sauce.