Place the chicken breasts in the bottom of the slow cooker.
In a mixing bowl, stir together the cream of chicken soup, chicken broth, diced green chiles with their liquid, garlic powder, cumin, and a pinch of salt and pepper. Pour this mixture over the chicken.
Cover and cook on low for 5 hours.
Remove the chicken, shred it with two forks, and return it to the slow cooker. Stir in the uncooked rice.
Cover and cook on low for 45 to 60 minutes more, until the rice is tender and has absorbed most of the liquid.
Turn off the heat, sprinkle the shredded pepper jack cheese over the top, and stir until the cheese melts into the mixture.