Make the chimichurri: combine garlic, parsley, cilantro, olive oil, lime juice, sea salt, and chopped white onion in a blender or food processor and blend to your desired texture (chunky or smooth).
Reserve 1/2 cup of the chimichurri for the marinade and extra sauce for serving.
Place the chicken in a large zip-top bag or airtight container and add 1/2 cup chimichurri; seal and toss to coat evenly. Refrigerate at least 15 minutes or up to 12 hours.
Preheat the grill to medium-high heat.
Grill the chicken skin-side down first and sprinkle with sea salt; cook until dark grill marks form, about 5–8 minutes.
Flip the chicken, sprinkle with sea salt, and continue grilling until the second side has dark grill marks, about another 5–8 minutes; continue turning as needed until drumsticks reach 165°F and thighs reach 165–175°F internal temperature.
If baking instead of grilling, preheat the oven to 375°F, place marinated chicken in a baking dish, and bake 45–60 minutes until internal temperature reaches 165–175°F. To crisp skin, broil 1–2 minutes on a high setting on the upper racks.
Transfer chicken to a serving platter and serve with the remaining chimichurri sauce alongside your preferred sides.