Heat olive oil in a large pot over medium-high heat.
Season chicken with salt and pepper, then brown for 4-5 minutes per side. Remove and set aside.
Sauté onions until translucent, then add garlic and cook until fragrant.
Add carrots and celery, cooking for 2-3 minutes.
Return chicken to the pot, pour in broth, and add bay leaves, oregano, and cumin.
Bring to a boil, then reduce heat and simmer for 25 minutes.
Add potatoes and corn, cooking until tender (15-20 minutes).
Remove chicken, shred the meat, discard bones and skin, then return meat to soup.
Taste and adjust seasonings.
Serve hot with garnishes.