Place peanuts in a spice or coffee grinder; process until medium ground.
Heat oil in a large Dutch oven over medium-high heat. Add onion; sauté 10 minutes or until lightly browned. Stir in ground peanuts, water, and next 5 ingredients (water through sweet potato); bring to a boil. Reduce heat, and simmer 15 minutes. Stir in chicken; cook 10 minutes or until chicken is done. Stir in cilantro.
Note: To make ahead, prepare the soup as directed, but stop before adding the cilantro. Cover soup and refrigerate up to two days. Let stand 30 minutes at room temperature; place in a saucepan over medium heat. Cook the soup until thoroughly heated; stir in cilantro.