Using a spiralizer or mandoline, make zucchini noodles, transfer into a large bowl and set aside. You can also chop zucchini into any size pieces, if you don't have the gadgets for making zucchini noodles.
Preheat large deep skillet on high heat and add chicken. Saute until golden brown, stirring occasionally. Add ½ teaspoon salt and ground black pepper towards the end along with apple cider vinegar, stir and cook for another minute. Transfer to a bowl and set aside.
Wipe clean or wash and pat dry the skillet and return to the stove on high heat. Spray with cooking spray and add zucchini noodles. Saute for 1½ minutes, stirring frequently.
Remove from heat and add previously cooked chicken, remaining salt, lime juice and cilantro. Stir gently and serve hot.