Heat oven to 400° F. Heat 1 tablespoon of the oil in a medium skillet over medium-high heat.
Add zucchini, onion, and corn and cook, stirring, until onion begins to soften, 3 to 5 minutes.
Transfer vegetables to a large bowl. Add chicken, Monterey Jack, 1 teaspoon salt, and ¼ teaspoon pepper. Mix to combine.
Wipe out the skillet and heat remaining oil over medium heat. Cook each tortilla until softened, 10 to 15 seconds per side. Transfer to a paper towel–lined plate.
Divide chicken mixture among the tortillas, roll them up, and place them in a baking dish, seam-side down. Bake until heated through, 8 to 10 minutes.
Meanwhile, in a food processor, pulse the tomatillos, jalapeño, cilantro, lime juice, and ½ teaspoon salt until finely chopped. Serve the enchiladas with the salsa and sour cream, if using.