Place the spinach leaves, olive oil, garlic, vinegar, oregano, lemon zest, lemon juice, salt and pepper in the work bowl of a food processor. Pulse repeatedly until the mixture forms a coarse paste. Transfer to a bowl and set aside.
Season the chicken with oregano, salt and pepper. Heat the vegetable oil in a large pan over medium-high heat. Add the chicken pieces in a single layer and sauté just until no longer pink in the middle ~ about 1-1/2 to 2 minutes per side. Sprinkle with lemon juice, transfer to a plate and set aside.
Preheat the oven to 450°F. Spray a 13-inch pizza pan with nonstick spray and place the pizza dough in the center. Flatten with the palm of your hand, then, using your fingertips, press and stretch the dough to form a 13-inch circle, creating a slightly thicker rim around the edge. Pinch out any air bubbles that may have formed.
Spread the pesto evenly over the crust to within 3/4-inch of the edge. Distribute the onion and pepper slices on top, then add the chicken. Top with the feta cheese, then the mozzarella.
Bake for 18 to 22 minutes, or until the cheese is bubbling and the crust is golden brown and crisp on the edges.
Remove from the oven and allow to rest for 5 minutes before cutting into wedges.
Tips for Making This Recipe
Be sure to just barely cook the chicken so that it doesn't dry out when you bake the pizza.