In The Chocolate War, do the Vigils have any loyalty for Trinity, or are their actions only designed to benefit themselves?
The existence of the Vigils is recognised by both Archie and the school administration alike as being essential for the survival of Trinity rather than just being an illegal school organisation that exists for its own purposes. There is definitely a sense in which the Vigils exists for its own reasons, and they are in part to cause licensed havoc in the school. This is shown by the pranks that Archie commands the various boys to do, such as unscrewing the furniture to the point where it all collapses easily and other such childish activities. However, at the same time, it is clear that the power the Vigils wield is recognised by Archie and the school administration. Consider, for example, the conversation Archie has with Brother Leon about the need to sell chocolates in order to support the school. Archie reflects on Leon's reasons for telling him about this scheme:
The Vigils kept things under control. Without The Vigils, Trinity might have been torn apart like other schools had been, by demonstrations, protests, all that crap.
So, as much as the Vigils do exist for their own reasons and purposes, at the same time they do perform a stabilising function within the school, demonstrating a loyalty to Trinity. There is evidence in the novel therefore that the Vigils are a chaotic organisation whose antics are put up with up to a point because of the way that they also do help Trinity and therefore demonstrate loyalty to it as an institution.