Preheat your oven to 375°F (190°C).
In a large pot, sauté the onion, carrots, and celery until the onion is translucent.
Add the cooked chicken, potatoes, chicken broth, thyme, salt, and pepper to the pot.
Bring the mixture to a gentle simmer, stirring occasionally for about 10-15 minutes.
Transfer the filling into a pie dish and cover it with the pie crust, sealing the edges.
Bake in the preheated oven for 30-35 minutes, until the crust is golden brown.
Remove from the oven and let it cool slightly before serving.