Preheat the oven to 425.
In a large pan, cook the bacon pieces until they are browned. Take the cooked bacon out and pour off most of the grease.
Add the onion and celery to the remaining bacon grease and cook, stirring, until soft. Return the bacon to the pan.
Add the thyme, pepper, and butter and cook until butter is melted. Add the flour and whisk, cooking for another few minutes.
Whisk in the chicken broth and continue cooking for a few more minutes until it thickens up. Stir in the chicken and potato and keep warm, stirring occasionally, until you're ready to use it.
Pour filling into bottom crust, cover with top crust, brush with beaten egg. Bake, uncovered, for about an hour. If it is browning too quickly, cover loosely with tin foil.