Heat 1 1/2 teaspoons oil in a large Dutch oven over medium-high heat. Add half of chicken; cook 5 minutes, browning on all sides. Remove chicken from pan. Repeat procedure with remaining oil and chicken. Remove from pan; cover and keep warm.
Add onion and carrot to pan; sauté 2 minutes. Stir in broth, corn, oregano, and thyme; bring to a simmer. Stir in baking potato and chicken; cover and simmer 20 minutes, stirring frequently to keep potato from sticking to pan. Add cubed potato; cover and simmer 20 minutes, stirring frequently. Stir in the cilantro and remaining ingredients, and cook, uncovered, 5 minutes, stirring frequently.