Heat olive oil in a large pot or Dutch oven over medium heat.
Add chopped onion and sauté until soft and translucent, about 4–5 minutes.
Stir in minced garlic and cook for 30 seconds until fragrant.
Add ground cumin, chili powder, smoked paprika, and oregano. Stir continuously for 1 minute to bloom the spices.
Add chicken breasts to the pot and pour in chicken broth. Ensure the chicken is fully submerged.
Bring the mixture to a gentle boil, then reduce heat to low. Cover and simmer for 20–25 minutes until chicken is fully cooked.
Remove chicken from the pot and shred it using two forks.
Return shredded chicken to the pot.
Add diced green chilies, cream cheese, and heavy cream. Stir until cream cheese is fully melted and incorporated.
Simmer uncovered for another 10–15 minutes, stirring occasionally, until the chili thickens.
Season with salt and black pepper to taste.
Stir in fresh lime juice just before serving.
Garnish with chopped cilantro and serve hot.