Sprinkle chicken evenly with salt and ground peppers.
Cook chicken in hot oil in a Dutch oven over medium heat 8 to 10 minutes or until brown on all sides. Remove chicken with a slotted spoon to a large bowl.
Add ham to Dutch oven, and cook, stirring constantly, 5 minutes or until lightly browned. Add ham to chicken; set aside.
Add onions and next 3 ingredients to Dutch oven, and cook 5 minutes, stirring to loosen any browned bits.
Drain tomatoes, reserving liquid. Stir reserved liquid and chicken broth into Dutch oven. Add chicken and ham; cover and cook over low heat 45 minutes.
Peel shrimp; devein, if desired.
Mash cooked garlic against side of Dutch oven, and blend into the mixture. Add shrimp, green onions, and remaining ingredients, and bring to a boil. Cover and reduce heat to medium low; simmer, stirring occasionally, 25 minutes or until rice is tender and liquid is absorbed.