Press the "sautee" button on your Instant Pot. Add the oil to the cooking vessel. Once hot, add the onions and cook for 2-3 minutes or until soft. Add the garlic and cook for 1 minute stirring constantly to prevent burning. Turn off the Instant Pot.
Add the chicken, chicken broth, corn, tomatoes with green chilis, black beans, chili powder, oregano, cumin, salt, pepper, and rice to the Instant Pot. Give everything a quick stir.
Cover and secure the Instant Pot lid. Be sure the release valve is set to seal. Press the "soup" setting button and then the "manual" button. Use the + and - buttons to set the soup for 15 minutes.
Once the Instant Pot has pressurized and cooked for 15 minutes it will beep that it's done. Turn off the Instant Pot and let it sit for 20 minutes. After 20 minutes, carefully turn the release valve to vent (use tongs or a kitchen towel to prevent scalding) and let the valve run until no more steam comes out. Carefully remove the lid.
Remove the chicken breasts to a plate and shred. Return to the pot and stir to combine. Ladle the soup into serving bowls and garnish as desired. Serve immediately.
If you prefer to use brown rice, use 2 cups pre-cooked rice in place of the uncooked white rice.