Rub the chicken with salt, pepper and oregano and one tablespoon olive oil and set aside for 30 minutes.
In a large heavy pot sauté the sofrito, onions and celery with remaining olive oil, for 5 minutes over medium-low heat. Brown the chicken pieces to seal in their flavor. Add the chicken stock or water to the chicken and bring to a boil. Cover, reduce heat and simmer for 10-15 minutes.
Raise the heat and bring to a boil once more; add carrots, potatoes, sazon and bay leaf. Reduce heat to medium and cook uncovered for 20 minutes, until carrot and potatoes are tender, stirring occasionally. During the last 5 – 10 , minutes add the angel hair and cook until pasta is done.