Combine in a bowl with the shallot, olive oil, vinegar, juice of the blood orange, salt and pepper.
Set aside about 1/2 cup of the marinade for later.
Place the chicken breasts in a zip-top bag. Pour in the remaining marinade. Seal the bag and massage the marinade into the chicken. Refrigerate for about 30 minutes.
Prepare the grill with a direct and indirect heat zone. The direct heat zone should be about medium to medium-high heat. You should be able to hold your hand about 5 inches over the coals for 4-5 seconds.
Add the marinated chicken to the grill, directly over the coals. Add the lid to the grill, and cook for 4 minutes.
Flip. Cover. Cook for another 4 minutes.
Move the chicken to the indirect heat zone. Continue cooking, until the internal temperature reaches 156F degrees, about 5-10 minutes.
Remove the chicken to a serving platter and top with the reserved chimichurri sauce.
Notes
If you don't care for cilantro, you can substitute flat-leaf parsley.