Place chicken in a pot and cover with water; bring to a boil and cook until chicken is no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Drain.
Place potato and carrot in another pot; cover with water. Bring to a boil; reduce heat and simmer until softened, about 15 minutes. Drain.
Place corn in a saucepan with 1/2 cup water. Bring to a boil; reduce heat; stir and cook until tender, 3 to 4 minutes. Drain.
Transfer corn to a food processor. Add chicken stock and puree until smooth, about 10 seconds. Add chicken, carrot, and potato. Puree until mixture is smooth and reaches desired texture.