In a large skillet over medium-high heat, heat 2 tablespoons of olive oil until it shimmers.
Add the chicken and cook for about 6 minutes, stirring, until browned. Remove the chicken from the skillet, and set aside on a platter, tented with aluminum foil to keep warm.
Return the skillet to the heat and heat the remaining 2 tablespoons of olive oil until it shimmers.
Add the onion and red bell pepper. Cook for about 5 minutes, stirring occasionally, until the vegetables are soft.
Add the garlic and cook for 30 seconds, stirring constantly.
Stir in the wine, and use the side of the spoon to scrape and fold in any browned bits from the bottom of the pan. Cook for 1 minute, stirring.
Add the crushed and chopped tomatoes, white beans, Italian seasoning, sea salt, pepper, and red pepper flakes. Bring to a simmer and reduce the heat to medium. Cook for 5 minutes, stirring occasionally.
Return the chicken and any juices that have collected to the skillet. Cook for 1 to 2 minutes until the chicken heats through. Remove from the heat and stir in the basil before serving.