Heat the oil and melt the butter in a skillet over medium-high heat until frothing, add the chicken, seasoned with salt and pepper to taste, and cook until lightly golden brown, about 3-5 minutes per side, before setting aside.
Add the garlic and red pepper flakes and cook until fragrant, about a minute.
Add the broth and deglaze the pan by scraping up any brown bits from the bottom with a wooden spoon while the broth sizzles.
Add lime juice and zest and season with salt and pepper to taste before removing from the heat and adding the cilantro and chicken.
