Preheat oven to 350 degrees F. Butter a 9 by 13-inch glass baking dish and set aside.
Bring a large pot of water to a boil add the pasta shells and cook for approximately 9 minutes until al dente. Drain and rinse under cold water being careful not to break the shells. Set aside.
Meanwhile prepare the filling. In a large bowl mix together the ricotta and Parmesan. Heat oil in a medium skillet over medium heat, add the garlic, and cook 1 minute, being careful not to brown it. Stir in the arugula until just wilted, about 2 minutes. Add the chopped chicken and stir well. Remove from heat and let cool for about 10 minutes. Add chicken mixture to cheese mixture and stir carefully. Stuff each shell with approximately 1/2 cup of the cheese filling and place in prepared baking dish.
For sauce, heat the butter in medium saucepan over medium heat. Add the garlic and cook for about 1 minute until fragrant but not brown. Add the flour and whisk until smooth. Gradually add the cream and milk and whisk until mixture begins to thicken and bubble. Remove from heat and add the chives, 1 cup Parmesan, cherry tomatoes and stir gently. Pour sauce over shells and sprinkle with remaining 3 tablespoons of Parmesan. Bake for 30 minutes until the sauce is bubbling and cheese is golden brown. Sprinkle with parsley.