In a bowl, mix together first 7 ingredients. Evenly sprinkle mixture on both sides of chicken breasts.
In a skillet heat butter and olive oil together over medium high heat. Sauté chicken until golden brown on each side, about 5 minutes on either side. Remove chicken and add lime juice and chicken broth to the pan, whisking up the browned bits off the bottom of the pan. Keep cooking until sauce has reduced slightly. Add chicken back to the pan to thoroughly coat and serve.