Preheat oven to 425F.
In the bowl of a food processor, add the shallots, parsley, thyme, marjoram, lemon zest, vinegar, salt and pepper. Pulse the machine to chop everything up then stream in the EVOO with the machine running until it forms a smooth paste. Transfer the mixture to a small bowl and reserve. Rinse out the processor bowl and return it to the machine base.
In a small bowl, mix up some salt, pepper, the paprika and garlic powder, and rub the seasoning all over the chicken pieces. Gently loosen the skin from the chicken pieces and rub half of the herb paste (chimichurri) under the skin of each. Transfer the chicken to a baking sheet and into the oven. Roast until golden brown and the juices run clear, about 45 minutes. Once the chicken has been in the oven for about 20 minutes, toss the chorizo into the oven along with the chicken and let it crisp up.
Serve the chicken with the remaining chimichurri for topping at the table and Piquillo Pepper Orzo and Olive Buttered Green Beans alongside.