In a 4- to 5-quart soup pot, over medium heat, heat olive oil.
Reduce heat to low and add onion. Sauté, stirring constantly, until softened and transparent, about 4 minutes.
Add garlic and oregano, and sauté for another minute, stirring constantly.
Add tomato and sauté for about 5 minutes, stirring periodically, until juices release.
Add chicken stock, raise heat, and bring to a boil.
Add potatoes and cilantro, and cover. Simmer until potatoes are tender (10-12 minutes).
Uncover pan, remove cilantro if you wish, and add chilies.
To serve, ladle into 12-ounce soup bowls, and garnish with fresh cilantro sprigs and a spoonful of crumbled Queso Fresco.
Accompany with taco chips and lime wedges.