Place the chicken breasts in the slow cooker. Add the black beans, corn, enchilada sauce, chili powder, and cumin. Stir gently to coat the chicken.
Cover and cook on low for 6 hours or on high for 3 hours, until the chicken is tender and shreds easily.
Remove the chicken from the slow cooker and shred it with two forks. Return the shredded chicken to the sauce and stir to combine.
Spoon the cooked white rice into four bowls. Top each bowl with the chicken mixture.
Sprinkle shredded cheddar cheese over each bowl. Add fresh cilantro leaves and serve with lime wedges on the side.