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 and cook 7–8 minutes total, turning once, until cooked through and no longer pink inside; transfer to a plate and tent with foil.
Reduce heat to medium and add the chopped onion to the same skillet; cook 1 minute, stirring.
Add the garlic and cook about 30 seconds until fragrant.
Pour in 1 cup chicken broth (or water), add the lime juice, chopped cilantro, red pepper flakes, and season with salt and pepper; bring to a gentle boil.
Simmer 8–10 minutes, until the liquid reduces by about 1/4 cup and flavors concentrate.
Whisk in 1/2 cup heavy cream (or chosen substitute) during the last minute of cooking and remove from heat.
Return the chicken to the skillet, spoon the sauce over it, and garnish with additional cilantro if desired before serving.