Prepare a medium-high gas grill or charcoal grill fire.
In large bowl, combine vegetables with oil, salt and pepper. Toss gently to coat. Grill, covered, until the veggies become tender and have grill marks on both sides (2-3 minutes per side). The chayote will become soft, but not limp, like the zucchini & squash.
Let vegetables cool slightly then slice crosswise into thin strips. Season to taste with salt & pepper. Assemble Tacos
Spoon some of the veggie mixture on top of each tortilla & top with a drizzle of the pesto and some crumbled cheese and chopped cilantro. Allow at least 2 tacos per person.