Heat olive oil in a large skillet over medium heat. Season the chicken thighs with salt, pepper, and paprika.
Once the oil is hot, add the chicken thighs to the skillet and brown them for about 5-6 minutes on each side. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and sauté for 3-4 minutes until it becomes translucent. Add the minced garlic and thyme, and cook for another 1-2 minutes.
Pour in the chicken broth and bring to a simmer. Stir in the heavy cream and return the chicken thighs back to the skillet.
Reduce the heat to low, cover the skillet, and let it simmer for 15 minutes until the chicken is fully cooked.
While the chicken simmers, prepare the rice according to package instructions.
Once the chicken is cooked through, remove it from the heat and let it rest for a few minutes. The sauce will thicken slightly upon cooling.
Serve the creamy smothered chicken over a bed of rice, garnished with fresh parsley if desired.