Place the chicken breasts into the Instant Pot liner.
Add the diced green chilies, cumin, oregano, salt, and pepper over the chicken. Pour the chicken broth over the ingredients. Do not stir excessively.
Secure the lid and set the valve to Sealing. Select Manual or Pressure Cook on High Pressure for 10 minutes.
When the cooking time finishes, allow a Natural Pressure Release (NPR) for 10 minutes. After 10 minutes, carefully switch the valve to Venting to release any remaining pressure (Quick Release).
Open the lid. Remove the chicken breasts and shred them using two forks. Return the shredded chicken to the pot.
Add the cubed cream cheese. Stir gently until the cream cheese is fully melted and the chili is creamy. Do not let it boil once the cream cheese is added.
Serve hot with your choice of toppings.
Notes
For a thicker chili, remove about 1 cup of the liquid and beans before adding the cream cheese, mash them, and stir the mixture back into the pot.
You can substitute Great Northern beans entirely with Cannellini beans or Great White Beans.
Toppings that work well include shredded Monterey Jack cheese, fresh cilantro, or a dollop of sour cream.