Grill both sides of the chicken breasts on medium-high heat for 10-12 minutes on a grill, until reaching internal cooked temperature of 165 degrees F. Set aside to cool and dice into small pieces.
In medium-sized bowl add half of the olive oil, lemon juice, salt and pepper and whisk.
Add arugula, tomatoes, onion, diced chicken, diced fresh mozzarella, parmesan cheese and mix together.
Then brush remaining olive oil on both sides of pizza crust.
Grill pizza crust on medium heat for about 1-1 1/2 minutes on each side, to create grill marks and warm up the crust.
Top with the salad mixture, cut, and serve.