Preheat the oven to 425.
In a large pan, cook the bacon pieces until they are browned. Pour off most of the grease.
Add in the onion and celery and cook until soft.
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 for about an hour.