Preheat your oven to 425°F (220°C).
In a saucepan, melt butter over medium heat.
Add onions and cook until translucent.
Stir in flour, salt, pepper, and thyme until well blended.
Gradually add chicken broth and milk, stirring constantly.
Bring the mixture to a boil, then reduce heat and simmer for 2 minutes.
Combine chicken, carrots, peas, and potatoes in a bowl.
Pour the sauce over the chicken mixture and stir until combined.
Roll out one pie crust and place it in a pie dish.
Fill the crust with the chicken mixture, then cover with the second crust and seal edges.
Cut slits in the top crust to allow steam to escape.
Bake for 30-35 minutes or until golden brown.