Pat chicken dry and season with 3/4 teaspoon salt and 1/2 teaspoon pepper. Heat butter in a wide, heavy 7 to 8-quart pot over moderately high heat until foam subsides, then brown chicken in 2 batches, skin side down first, turning occasionally, about 10 minutes. Transfer chicken as browned to a plate.
Add onion to pot, along with oregano and 1 teaspoon each salt and pepper, and saute, stirring, until light golden, about 5 minutes. Peel and coarsely grate the baking potatoes with a box grater, and add to the pot. Add back the chicken, broth, and water. Simmer, covered, stirring occasionally, until chicken is cooked through, about 25 minutes.
Transfer chicken with tongs to a cutting board to cool. Drain the cubed yellow potatoes and add to pot. Simmer, covered, stirring occasionally, until cubed potatoes are almost tender, about 10 minutes. Add corn and simmer, covered, until tender, 5 to 10 minutes more. While corn is cooking, remove skin and bones from chicken and coarsely shred meat. Add meat to pot and heat through.
Serve stew with accompaniments in separate bowls.
Recipe courtesy of Gourmet Magazine