Heat olive oil in a large non-stick skillet over medium-high heat. (I used a 12-inch cast iron skillet)
Add cubed chicken pieces; cook until browned on all sides, about 3 minutes.
Add onions and peppers.
Season with salt, ground pepper, and fresh thyme leaves.
Continue to cook, stirring occasionally, until vegetables are tender; about 6 minutes.
Stir in garlic, water, rice, and sour cream; stir until well blended.
Bring mixture to a boil.
Add tomatoes and season with paprika.
Lower heat to a simmer, cover the pan, and continue to cook for about 7 minutes, or until rice is tender.
Remove from heat; stir in cheese and garnish with green onions and parsley.
Taste for seasonings and adjust accordingly.
OPTIONAL: For a browned, crusty top, you can pop the skillet under the broiler for a minute or 2.