Heat olive oil in a large skillet over medium heat.
Season the chicken breasts with salt, pepper, and thyme, then add to the skillet.
Cook the chicken for about 6-7 minutes on each side until fully cooked, then remove from skillet and set aside.
In the same skillet, add chopped onion and sauté until translucent, then add minced garlic and cook for another minute.
Add chicken broth to the skillet, scraping the bottom to deglaze, then bring to a simmer.
Stir in the heavy cream and return the chicken to the skillet, reducing heat to low.
In a separate pot, cook the rice according to package instructions.
Once rice is cooked, add it to the skillet, stirring to combine, and allow it to absorb the sauce for about 5 minutes.
Serve warm, garnished with fresh herbs if desired for an added touch of color and flavor.