In a large pot or Dutch oven, heat the olive oil over medium-high heat.
Season the chicken thighs with salt and pepper. Add to the pot and cook until browned on both sides, about 3-4 minutes per side. Remove the chicken and set aside.
In the same pot, add the diced onion and cook until translucent, about 5 minutes. Add the minced garlic and cook for an additional minute until fragrant.
While the onion is cooking, blend the tomatillos in a food processor or blender until smooth.
Return the chicken to the pot with the onions and garlic. Add the pureed tomatillos, green chilies, chicken broth, ground cumin, dried oregano, and ground coriander. Stir to combine.
Bring the mixture to a boil, then reduce heat to low and simmer, covered, for 45 minutes, or until the chicken is very tender.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
Stir in the heavy cream and cook for an additional 10 minutes, allowing the chili to thicken slightly.
Taste and adjust seasoning with salt and pepper if needed. Serve hot, garnished with chopped cilantro and lime wedges on the side.