Rinse and pat dry the chicken and season with salt and pepper to taste.
Set the pressure cooker to saute and heat the oil. Working in batches, sear the chicken until for about 3 - 4 minutes per side or until golden brown. Transfer the chicken to a plate; set aside.
Add the onions and saute for about 3 minutes or until the onions start to soften (add additional oil if needed). Add the carrots, bell peppers and garlic and cook for about 2 minutes. until they melt. Add the oregano, thyme and Italian seasoning and cook for 1 minute or until fragrant.
Pour in the wine and deglaze the pot, scraping the browned bits from the bottom with a wooden spoon. Bring to a boil and cook for about 2 - 3 minutes. Stir in the crushed tomatoes, broth and bay leaf. Add the chicken back to the pot and press cancel.
Secure the lid, turn the valve to sealing and cook on HIGH pressure for 14 minutes. When done, allow the pressure to release naturally for 10 minutes. Carefully release the remaining pressure and open the lid.
Stir in the olives, capers, chopped basil, chopped parsley and red pepper flakes. Taste and if needed, stir in the chicken bouillon granules. Season to taste with salt and pepper.