Pat the chicken breasts dry and season both sides generously with salt and pepper.
Heat 1 tablespoon oil in a large heavy-duty skillet over medium-high heat until shimmering.
Add the chicken to the skillet and cook 7–8 minutes, turning once, until cooked through and golden; transfer to a plate and cover with foil to keep warm.
Reduce heat to medium, add the chopped onion to the same skillet and cook about 1 minute until softened.
Add the garlic and cook 30 seconds more, stirring so it doesn't burn.
Pour in the chicken broth, lime juice, chopped cilantro, red pepper flakes, and season with salt and pepper; bring to a gentle boil.
Simmer uncovered 8–10 minutes, or until the liquid reduces by about 1/4 cup and slightly thickens.
Whisk in the cream during the last minute of simmering, then remove the skillet from heat.
Return the cooked chicken to the sauce, spooning sauce over the pieces to warm and coat them.
Garnish with additional cilantro if desired and serve immediately with rice or steamed vegetables.