In the bottom of a heavy pot, heat the olive oil over medium heat. Season the chicken with salt, pepper, and adobo. Cook the chicken on each side until browned, about 3 minutes each side. Remove the chicken from the pot and set aside in a dish, (chicken is not fully cooked yet).
With the heat still on medium, add the onion, carrots, celery, and garlic to the pot. Cook until vegetables soften, stirring every so often, for about 5 minutes. Add the chicken back to the pot and pour in the chicken stock. Bring to a boil, and then reduce the heat to low. Cook for about 45 minutes.
Remove the chicken from the pot again and place in a dish. Bring the stock to a boil. Pour in the pasta and stir. While the pasta cooks, remove the chicken meat from the bones and shred into bite sized pieces.
Once the pasta is cooked, turn off the heat. Stir in the chicken and parsley.
Store in airtight containers in the refrigerator for up to 5 days.