Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the rice is tender and liquid has been absorbed, 20 to 25 minutes.

Preheat the oven to 350 degrees F (175 degrees C).

Pour just enough water into a large skillet to cover the bottom in a shallow layer; add chicken pieces in a single layer. Season chicken with salt and pepper. Turn heat to medium-high and cook chicken until no longer pink in the center and the juices run clear, adding water as needed to keep pan wet, 7 to 10 minutes; drain liquid.

Stir cooked rice, cooked chicken, cream of chicken soup, milk, and Mexican blend cheese together in a casserole dish. Smooth the top of the mixture with the back of a spoon. Arrange biscuit dough over the rice and chicken mixture, breaking dough pieces as needed to get maximum coverage and to avoid overlap.

Bake in the preheated oven until the biscuit topping is golden brown and the bottom layer is heated through completely, 20 to 35 minutes.