In a food processor, add the parsley, tomatoes, and 1/3 cup of the chicken cooking liquid. Process until the tomatoes are crushed but not pureed.
Transfer the mixture to a bowl. Add the onion, garlic, vinegar, olive oil, and whisk well. Season with salt and pepper to taste.
For the traditional style of serving: Transfer the chicken and chorizo to a cutting board. Carve the chicken (if using a whole), slice the chorizo, and arrange on a serving platter. Pour some cooking liquid over. Now transfer all the veggies and chickpeas (using a slotted spoon) to another plate. Discard the onion, celery, garlic, and bay leaf. Once again pour some cooking broth over. Serve accompanied by the sauce.
Alternatively, you can simply serve the meats, veggies, and chickpeas in one bowl drowned in the cooking liquid. Enjoy!