Shred zucchini using the large holes of a box grater. Squeeze dry in a clean kitchen towel (you should have about 2 cups).
Heat oil in a large nonstick skillet over medium-high heat. Saute the onion until soft. Add the zucchini, chili powder, cumin and salt and cook for 5-7 minutes.
Place mixture in bowl to let cool.
Add shredded chicken, cheese, and cilantro and stir to mix.