Heat the olive oil in the Instant Pot using saute mode. When the pot is hot, add the onion and cook, stirring occasionally, for 2-3 minutes, until softened.
Meanwhile, put 1 cup of the white beans and 1 cup of the chicken broth in a blender or food processor and puree until smooth.
Press Cancel to turn off the Instant Pot and add the minced garlic. Cook, stirring, for 30 seconds. Pour in about 1 cup of the chicken broth and stir, scraping up any bits stuck to the bottom of the pot.
Add the pureed beans and broth, diced green chiles, cumin, chili powder, oregano, salt, cayenne pepper and 2 cups of the remaining broth to the Instant Pot (reserve the remaining ½ cup of broth to add after cooking if you want your chili thinner). Stir. Add the chicken breasts and remaining beans to the pot.
Close the Instant Pot lid and turn the steam release valve to the sealing position. Pressure cook at high pressure for 14 minutes (18 minutes for frozen chicken breasts). The Instant Pot will take about 15-20 minutes to reach pressure and then the cook time will begin counting down.
When the cook time ends, allow the pressure to release naturally for 10 minutes by leaving the Instant Pot alone. Then release the remaining pressure by carefully turning the steam release valve to the venting position.
Once all of the steam has escaped and the pin drops down, open the Instant Pot lid. Remove the chicken to a clean bowl, plate or cutting board. Let the chicken cool for a few minutes and then shred and return it to the chili. Stir in the corn. Serve chili with toppings, as desired.