If the chicken breasts are uneven in thickness, pound or slice them down so they're all even. This way all the breasts will cook through simultaneously. Sprinkle each with salt and pepper.
In a large skillet, heat the oil over medium-high heat. Add the chicken and cook for 6-7 minutes, turning once. You want the chicken nice and browned on the outside. Set chicken on a plate and cover.
Remove skillet from heat and add the broth, lime juice, onion, cilantro, and red pepper. Return to heat. Cook and stir to scrape up the browned bits from the bottom of the skillet. Bring to a boil. Allow to boil gently, uncovered, for 10 minutes or until the liquid is reduced to around 1/4 cup. (During this time you can steam or sauté some veggies to have on the side. We like to sauté green beans.) Reduce heat to medium-low, then add the cream and butter. Stir until butter has melted.
Add chicken to the sauce and uncovered and bathe the chicken in the juices for about 5 minutes. Serve chicken with sauce spooned on top and any of the listed optional garnishes.