Place the chicken, broth, and water in a large pot. Set the pot over medium heat.
Once the mixture starts boiling, add the rice. Remember to keep the seasoning packet aside for now. After adding the rice, cover the pot and turn off the heat.
In a small bowl, mix together flour, salt, and pepper.
Next, heat butter in a medium saucepan over medium heat.
Stir in the seasoning packet that was set aside earlier. Keep stirring until the mixture gets bubbly.
Turn the heat to low. Now, gradually add the flour mixture to the butter. Do this a few tablespoons at a time. Keep stirring all the while, so you get a smooth mixture called a roux.
Slowly whisk in the cream into this roux. Add it a little at a time and keep whisking until it's fully mixed in and smooth.
Cook this cream mixture for about 5 minutes, or until it gets thicker.
Now, it's time to add the flour and cream mixture to the broth and rice in the large pot.
Cook everything together over medium heat for about 10 to 15 minutes, or until it's all heated through and ready to serve.