Spiralize zucchinis or julienne them lengthwise using a mandolin.
Heat one tablespoon of olive oil in a large skillet over medium-high heat and add the zucchini noodles. Saute them for about 3 minutes until cooked but still slightly crunchy.
Transfer them to a colander to drain off the excess liquid.
Wipe off any moisture from the skillet and add one tablespoon of olive oil. Heat over medium-high heat and add the shredded chicken. Saute until slightly brown.
Add the chopped onion, parsley, and cherry tomatoes to the skillet and cook until the tomatoes become soft.
In a small bowl, combine the lemon juice, minced garlic, remaining tablespoon of oil, salt, and pepper.
Return the zoodles to the skillet and add the lemon juice/olive oil mixture. Cook for 2-3 minutes and serve. Top with grated parmesan cheese.