To make zucchini spirals, julienne them using a mandolin or a spiralizing tool.
Saute the zoodles: heat one tablespoon of olive oil in a large skillet over medium-high heat and saute the zoodles for about 3 minutes. They should be cooked but still a bit crunchy. Do not overcook them.
Place the zoodles in a colander and let them drain the excess liquid.
Using a paper towel, wipe down the skillet, add another tablespoon of olive oil and saute the onions and cherry tomatoes for about 2 minutes. Add the shredded chicken and parsley and cook until the tomatoes are soft.
Make the sauce: in a small bowl combine the lemon juice, garlic, salt, pepper, and remaining tablespoon of olive oil.
Drizzle the sauce over the chicken, add the drained zoodles, and cook for about 2-3 minutes until all is heated through. Mix in the parmesan cheese and serve while hot.