Whisk together all of the ingredients for the chimichurri sauce in a small bowl and set aside.
Place the chicken legs in a medium bowl, add half of the chumichurri sauce and smother over chicken legs. Cover the bowl and refrigerate for at least several hours, or better yet, overnight and up to 24 hours.
Reserve the other half of chimichurri sauce for serving the chicken legs.
Preheat the grill to 300F at the grate level. Basically, the grill should not be very hot.
Remove chicken legs from the bowl and pat dry with paper towels. Some bits and pieces of herbs and chili pepper remaining on the skin are totally fine, but you want as much of the liquid and oil off as possible for better browning. Oil will also so drip can cause flare-ups. Discard any leftover chimichurri marinade.
Grill chicken legs over direct heat, flipping frequently, about every 3 minutes, until the chicken is cooked through and internal temperature has reached a minim of 165F.
Let the chicken rest for 3 minutes and serve with the reserved chimichurri sauce.