Lay the raw chicken breasts evenly across the base of the slow cooker.
In a mixing bowl, whisk together the condensed cream of chicken soup, chicken broth, and powdered gravy mixes until a smooth consistency is achieved.
Pour the prepared gravy blend over the chicken in the cooker. Cover with the lid and cook on the low setting for approximately 4 hours.
Once the internal temperature of the chicken reads 165°F, transfer the cooked meat to a cutting board and use forks to shred into bite-sized pieces.
Add the sour cream to the remaining gravy in the crockpot, whisking until thoroughly incorporated and smooth.
Return the shredded chicken to the crockpot and stir until all pieces are fully coated with the creamy gravy mixture.
Serve warm atop your chosen side dish, and sprinkle with freshly chopped parsley just before serving.