Preheat oven to 425 degrees. Heat the olive oil in an oven-safe skillet. Once hot, add the chicken and cook until the chicken is firm and cooked through. Drain off any excess liquid and add the onion, garlic, potatoes, and carrots. Cook, stirring often, for about 5 minutes or just until the onions are translucent and the carrots and potatoes begin to soften.
Stir in the peas and flour. Make sure to coat all the ingredients in the flour. Gradually stir in the chicken broth and bring to a simmer to thicken. Add the salt, pepper, and thyme.
Remove from heat and top with the pie crust, tucking the edges into the pan. Cut about 4 slits in the top of the crust and bake for 15 to 20 minutes or until the crust is golden brown. Let the pot-pie sit for about 10 minutes before serving.