To prepare the pastsy: put the flour and chives in a bowl. using your fingertips, work in the butter until the mixture looks coarse crumbs. Add the cheese and toss it together with the flour mixture just until evenly mixed.
In a small bowl whisk together the egg yolks and 5 tablespoons of cream. While stirring the flour-butter-cheese mixture continuously with a fork, pour in the yoke-cream mixture a little at a time.
If mixture is dry add remaining cream., knead the dough lightly until it is smooth. Press the dough into a thick flat disk, wrap in plastic wrap and refrigerate until needed.
The filling: Heat a large skillet over medium -high heat and add the butter. Add chicken pieces and saute just until lightly browned but not yet cooked through. remove chicken to a mixing bowl. leave the butter in skillet and saute the carrots and celery and mix vegetable about 5 minutes. set aside.
For the sauce, melt butter over medium heat. Add flour and whisk until the mixture is smooth and bubbling, about 2 minutes, Remove the skillet from the heat and gradually whisk in the stock, cream, and thyme. Return the skillet to the heat and, stirring consantly, bring the mixture to a simmer. Cook, stirring continuosly, until the sauce has thickened and smooth, about 2 minutes. Season to taste with salt and pepper. set aside to prepare crust.
Preheat oven to 375 degree.roll out bottom pie crust and pour in the filling and then roll out top crust cut into to strips and crisscross dough strips, cutting to make edges smooth.. Bake the pie until the crust is golden brown and the filling beneath is bubbling hot, about 45 minutes.