In a small bowl combine the chicken, garlic, cilantro, lime juice, 1 tablespoon extra virgin olive oil, sea salt, and black pepper. Cover the bowl with plastic wrap and place it inside of the refrigerator. Allow chicken to marinate for 4 to 12 hours.
Preheat an electric pressure cooker using the Sauté function, press the button multiple times until the display panel reads MORE. When the display panel reads HOT add 1 tablespoon extra virgin olive oil and arrange the chicken breasts in a single layer on the bottom of the pot.
Allow the breasts to cook for 5 minutes on each side. Add 1/4 cup chicken broth, then place the lid on the pressure cooker. Make sure the vent valve is in the SEALING position. Select the MANUAL/PRESSURE COOK function and HIGH PRESSURE. Use the +/- buttons until the display reads 6.
When the cooker beeps to let you know it's finished, let it naturally release the pressure for 5 minutes before switching the vent valve from the SEALING to the VENTING position. Use caution while the steam escapes, it's hot.
Carefully remove the chicken from the cooker and serve warm.