Preheat the oven to 375°F (190°C).
If needed, pound the chicken breasts to an even thickness. Season both sides with salt and black pepper.
Heat olive oil in a large ovenproof skillet over medium-high heat.
Add the chicken and cook for 6–7 minutes, turning once, until nicely browned on both sides. Transfer to a plate and loosely cover with foil.
Remove the skillet from heat and add chicken broth, lime juice, red onion, cilantro, and red pepper flakes.
Return the skillet to the heat and scrape up any browned bits from the bottom.
Bring the mixture to a boil and cook uncovered for 10–12 minutes, or until reduced to about 1/2 cup.
Reduce the heat to medium-low. Stir in the heavy cream and butter until smooth and fully combined.
Return the chicken to the skillet, turning to coat with the sauce. This Creamy Cilantro Lime Chicken develops its signature flavor as the chicken absorbs the creamy citrus sauce.
Transfer the skillet to the oven and bake uncovered for 5–10 minutes, or until the internal temperature reaches 165°F (74°C).
Spoon extra sauce over the chicken before serving.
Garnish with lime wedges and fresh cilantro if desired.