Preheat your oven to 400°F and lightly grease a small oven-safe baking dish with the olive oil.
Wash and peel the potato, then slice it into very thin rounds using a mandoline or a sharp knife.
Cut the chicken breast into small, bite-sized cubes or thin strips.
In a small mixing bowl, whisk together the coconut milk, chicken broth, nutritional yeast, arrowroot powder, minced garlic, sea salt, black pepper, and fresh thyme until smooth.
Layer half of the potato slices in the bottom of the prepared baking dish, then top with the chicken pieces.
Place the remaining potato slices over the chicken in an overlapping pattern.
Pour the coconut cream mixture evenly over the potatoes and chicken, ensuring the liquid seeps into the layers.
Cover the dish tightly with foil and bake for 30 minutes.
Remove the foil and bake for an additional 15 to 20 minutes until the potatoes are tender and the top is lightly browned and bubbling.
Let the dish rest for 5 minutes before serving to allow the sauce to thicken.