In a small bowl, combine the first 7 ingredients.
Sprinkle mixture on both sides of chicken breast halves.
In a skillet, heat butter and olive oil together over medium-high heat.
Saute chicken until golden brown, about 5 minutes on each side.
Remove from skillet and keep warm.
Add lime juice and chicken broth to the skillet, whisking up all of the browned bits from the bottom of the pan.
Cook until the sauce has reduced slightly.
Return chicken to the skillet to thoroughly coat with the sauce; serve.