Place a large skillet over medium heat. Add the butter and once melted, add the chicken breasts. Sear the chicken for 5 minutes per side. Then remove the chicken from the skillet and set aside.
In the same skillet, sauté the onions and garlic for 2-3 minutes. Pour in the diced red peppers and sauté another 1-2 minutes. Then add the chicken broth, cream cheese, and crushed red pepper. Simmer and stir to melt the cream cheese into the broth.
Once the sauce is smooth, add the chicken breasts back to the skillet to warm. Stir in the chopped basil and simmer another 2 minutes before serving. Salt and pepper to taste. Slice and serve the chicken covered in the creamy pan sauce.