Set the Instant Pot to Sauté mode. Add olive oil.
Add chicken breasts and season with salt and pepper. Brown on both sides.
Turn off Sauté mode, add 1 cup of chicken broth, and secure the lid.
Set the pressure valve to Sealing. Press Manual and cook for 10 minutes.
Once done, do a quick release of pressure. Open the lid and stir the chicken.
Add the remaining 4 cups of chicken broth, onion, garlic, green chiles, navy beans, garlic salt, seasoned salt, pepper, chili powder, cumin, and smoked paprika. Stir to blend.
Secure the lid, set the pressure valve to Sealing, and press Manual for 15 minutes.
After cooking, let it sit for 10 minutes before doing a quick release.
Remove the chicken breasts, shred them, and return to the pot.
Stir in cream, cream cheese, and shredded cheese until melted. Stir in chopped cilantro.
Serve the chili with chips, sour cream, onions, and extra cheese if desired.