Zest the entire lime and then cut in half. Remove the seeds from the red pepper and chop into chunks.
While the chicken is cooking (see below) or in the days before (up to 5 days in advance), you can prepare your Chimichurri Rojo in a mini food processor. Just add the olive oil, vinegar, lime juice from 1/2 the lime, garlic clove, parsley, cilantro leaves, salt and pepper. Cover and pulse until the herbs have blended enough to make room for the red pepper.
Add the red pepper chunks, then cover the processor and pulse to get it started, then blend until everything is about the same size and the there are no large chunks of garlic.
Last, stir in the lime zest. Store in the fridge until ready to serve and eat!
Season each side of the chicken breasts with olive oil, salt, and pepper. Place under broiler (High) for 6-7 minutes or until you start to see a black char on the top of the chicken. Then take them out and flip them. Put them back under the broiler for another 6-7 minutes.
When the chicken is done cooking, let it rest for about 5 minutes so that the juices soak back into the chicken and it stays moist. You can serve 1 breast per person, but I like to slice them all on a bias and serve each person 3-4 slices to start. Spoon the Chimichurri Rojo over top (it can be served cold or room temperature) and Enjoy!
While there are only 4 chicken breasts in this recipe, if you slice the chicken, you can easily extend the serving size to 5 or 6 by giving each person 3-4 slices.