Place the chicken breasts in the bottom of the slow cooker.
Add the rice, chicken broth, cream of chicken soup, salt, and black pepper. Stir everything together so the rice is mostly covered with liquid.
Cover and cook on low for 4 to 5 hours, until the chicken is cooked through and the rice is tender.
Remove the chicken, shred or cut it into bite-sized pieces, then return it to the slow cooker.
Stir in 1 cup of the shredded cheddar cheese until melted. Sprinkle the remaining 1/2 cup cheese over the top, cover for 5 minutes to let it melt, then serve.