In a gallon size Ziploc bag or large bowl, combine chicken and cilantro mixture; marinate for at least 2 hours to overnight, turning the bag occasionally. Drain the chicken from the marinade.
In a medium bowl, combine cilantro, 2 tablespoons olive oil, lime juice, lime zest, chili powder, cumin, salt and pepper.
Working in batches, add chicken to the grill pan in a single layer and cook until golden brown and cooked through, reaching an internal temperature of 165 degrees F, about 4-5 minutes per side. Serve immediately.
Heat the remaining 1 tablespoon olive oil in a cast-iron grill pan over medium-high heat.