Sprinkle chicken evenly with sea salt and pepper. Heat oil in a large skillet over medium-high heat. Add chicken and lime slices, and cook 3 to 4 minutes or until lightly browned. Add lime juice; turn chicken, and cook 3 to 4 minutes more. Remove chicken and lime slices to a plate.
Add garlic to skillet, and cook, stirring constantly, about 30 seconds; add wine, scraping browned bits from bottom of pan. Add chicken broth, and cook 5 to 7 minutes or until reduced by half. Return reserved chicken, lime slices, and any juices to pan. Reduce heat to low, and simmer 15 minutes or until chicken is cooked through. Remove from heat; sprinkle with cilantro, and serve warm with Salsa Verde.