Preheat oven to 400º. Bring a large pot of salted water to boil for the pasta.
Meanwhile, in a large skillet, 12" non-stick if you have it, heat the olive oil over medium heat.
Add the onion and cook just until it begins to soften (about 5 minutes).
Add the slices of zucchini, spreading them out in the pan. Cook just until it begins to soften, another 5 minutes.
While the onion and zucchini are cooking, use kitchen shears to crush the whole tomatoes inside the can.
Make sure to take scissors all the way to the bottom of the can.
Add salt to the zucchini in the skillet, add the crushed tomatoes. Bring the sauce to a boil.
Toss in chicken that has already been cooked. I chopped the chicken into bite-size portions.
Simmer just until it thickens, about 8-10 minutes. If the sauce is too thick, add 1/4 cup water, bring back to simmer. I did not add any additional water to my sauce.
Don't let the zucchini begin to fall apart. Turn off heat. Toss in chopped basil.
As for the pasta, only cook the rigatoni until al dente, a few minutes LESS than the package directions.
Drain the pasta. Mix drained pasta with your sauce. I used the same pot I cooked the pasta in.
Butter a 9 x 13, large baking dish. In a medium bowl, toss and mix up the two kinds of cheese.
Spread half the pasta and sauce mixture into the baking dish.
Top with half the cheese mixture.
Layer remaining pasta and sauce, then remaining cheese.
Bake, uncovered, until browned and bubbly, about 20-25 minutes.
Remove from the oven. Allow to stand and rest for 5-6 minutes before serving. Serve with bread or a simple salad.