Heat the olive oil in a large pot over medium heat. Add the ground turkey and cook until it is no longer pink, breaking it up with a spoon as it cooks.
Add the diced onion and cook for 3 minutes until it starts to soften. Stir in the minced garlic and chipotle peppers and cook for 1 minute.
Sprinkle in the cumin and oregano, then pour in the diced tomatoes with their juices. Stir everything together.
Add the chicken broth, salt, and black pepper. Bring the soup to a boil, then reduce the heat and simmer for 15 minutes.
Ladle the soup into bowls and serve with lime wedges and chopped cilantro.