Heat the oil in a large Dutch oven over medium-high heat. Add chicken to pan; cook 5 minutes, browning on all sides. Add potato and next 6 ingredients (through salt); stir well. Add broth; bring to a boil. Cover, reduce heat, and simmer 45 minutes or until chicken is done.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and water, stirring with a whisk until smooth. Add flour mixture and peas to pan. Bring to a boil; cook 5 minutes. Remove chicken from pan; cool slightly. Remove chicken from bones; discard bones. Return chicken to pan; stir to combine.