Mix in grated zucchini and season with salt and pepper.
Heat the oil in a small, non-stick skillet. When hot, add half the egg mixture and cook for 1 minute until the egg begins to set. Scatter evenly with half diced chicken.
Cook for a further 1-2 minutes, until the egg is golden underneath, and just set on top. Slide out onto a serving plate, folding it over as you go. Repeat.