For the lemon-oregano vinaigrette: Combine the olive oil, lemon juice, vinegar, oregano and salt and pepper to taste in a small jar. Cover, shake well and set aside.
For the salad: Put the arugula in a large salad bowl. Add the tomatoes, parsley, cucumber and peppers and toss well.
Heat a medium skillet over medium-high heat. Rub the olive oil over the pizza crust, distributing it on both sides. Place the crust in the skillet and heat for about 2 to 3 minutes on each side, being careful not to burn. Remove and cut into approximately 1 1/2-inch pieces.
Put the chicken and crust pieces on top of the salad. Add the feta and pour the vinaigrette over the top. Toss well before serving.