Cut chicken into small bite sized pieces. Melt butter or olive oil in skillet, add chicken, onions, bell pepper, garlic and celery. Let saute until chicken is done. Add the tomatoes, basil, parsley and pepper toward end of cooking process and let simmer for about 5 minutes until hot through and through. Set to the side, let cool long enough to get food processor ready. Pulse chicken mixture into very small pieces.
Melt cream cheese to a stirable state in the microwave and then add hot chicken mixture, stir to combine. Add beaten eggs and stir again. The heat from the chicken will help with any lumps in the cream cheese.
Pour mixture into deep dish pie crust then bake at 350°F until set in center and golden brown around the edges 40-50 minutes. Be sure and take the pie out when it has just set, much like a cheesecake, your pie will continue to cook for about 5-10 minutes after being removed from the oven. Place on wire rack to cool and set. Serve room temperature or chilled. Cooking time may vary more or less depending on the heat of your oven.