Heat oven to 400° F. Heat 1 tablespoon of the oil in a medium skillet over medium-high heat. Add the zucchini, onion, and corn and cook, stirring, until the onion begins to soften, 3 to 5 minutes. Transfer to a large bowl.
Add the chicken, Monterey Jack, 1 teaspoon salt, and 1/4 teaspoon pepper. Mix to combine.
Wipe out the skillet and heat the remaining oil over medium heat. One at a time, cook the tortillas in the oil until softened, 10 to 15 seconds per side. Transfer to a paper towel-lined plate.
Divide the chicken mixture among the tortillas, roll them up, and place seam-side down in a large baking dish. Bake until heated through, 8 to 10 minutes.
In a food processor, pulse the tomatillos, jalapeño, cilantro, lime juice, and 1/2 teaspoon salt until finely chopped. Serve the enchiladas with the salsa and sour cream, if using.