Preheat your oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat.
Add sliced onions and sauté until caramelized, about 15 minutes.
Season chicken breasts with salt, pepper, and thyme.
Push onions to the side and add chicken to the skillet, browning on both sides.
Stir in the rice, then pour in the chicken broth.
Bring to a simmer, then transfer the skillet to the preheated oven.
Bake for 25 minutes or until chicken is cooked through.
Remove from the oven and sprinkle with Gruyère cheese.
Return to the oven for an additional 5-10 minutes until cheese is melted and bubbly.