Heat the oil in a dutch oven or large pot over medium-high heat.
When oil is hot add the onion and cook, stirring occasionally, until softened, about 5 minutes.
Add the jalapeno, garlic, oregano, cinnamon, allspice, peppercorns, and kosher salt to the pot. Stir and cook until fragrant, about 20 seconds.
Pour in the chicken stock and bring to a boil.
Add the chicken to the pot, stir and return to a boil.
Cover the pot and reduce heat to medium-low. Cook, stirring occasionally, about 20 minutes.
Cut 1 lime into wedges and set aside for garnish.
Add the juice from the remaining 2 limes into the soup and stir. Add salt and pepper to taste.
Serve the soup garnished with the lime wedges, fresh chopped cilantro, and tortilla chips.
