Heat the olive oil a large stockpot over low heat. Add the onion and poblano. Cook until the onion is translucent, about 3 minutes. Add the garlic and jalapeno; cook until fragrant, 45 to 60 seconds.
Stir in the tomatoes and oregano and cook for 5 minutes more. Turn the heat to high, add the chicken stock, and bring to a boil. Turn the heat to low, cover, and cook for 30 minutes.
Add the chicken and cook for another 5 minutes.
Just before serving, add the lime juice to the soup. Taste and adjust the seasoning, adding more salt, pepper, jalapeño, or lime juice if needed.
Ladle the soup bowls and top with two or three tortilla chips. Serve with garnishes on the side.