Warm up the grill to medium heat.
Combine the rub ingredients in a small bowl.
Brush the chicken, zucchini, and corn with oil.
Season the chicken with the rub.
Grill the chicken and vegetables over medium heat with the lid closed for 8-10 minutes or until tender. The chicken should be firm. the zucchini should be barely tender, and corn kernels golden brown in spots.
Remove the chicken and veggies from the grill and allow to cool.
Cut the chicken and zucchini into ¼ inch chunks. Cut the corn kernals from the cob.
In a large bowl, combine the zucchini and corn with the chopped oregano, garlic, and lime juice. Season the mixture with salt and pepper. Add the chicken and stir to combine.
In a small bowl, smash together the guacamole ingredients and set them aside.
Lay the tortillas on a cookie sheet and fill with equal amounts of the vegetable mixture and cheese. Fold the tortillas in half.
Grill the quesadillas over low heat for 3-4 minutes per side. Flip the quesadilla once during cooking. Note: They are a bit thick so make sure the tortillas don't get burned before the insides are cooked.
Transfer the quesadillas to a cutting board and cut them into strips or wedges. Serve with guacamole.