Grand Leader

"You wouldn't think an organization called the Chaos Coalition would have a leader."
"No. You really wouldn't. And yet, here is one. Very public and officially labeled and everything."

Every formal organization is required to have a leader. In most situations, it's just essential that there's someone to make the final decisions.
In this case, it's crucial that someone takes the attention.

The Ultimate Patsy

The Chaos Coalition does periodically require leadership. It's more of a council, and of that council it's more a rotating position. There are people who have more authority than others, usually based on seniority. On the whole, I really don't know why people assume that an organization literally named for its erratic nature would have anything approaching a formal leadership structure. Therefore, the "leader" of the Coalition is less likely to have any real authority. Not quite the lowest ranking member, since you don't want to put all that pressure on someone new or inexperienced or less committed than the rest. But the Grand Leader of the Chaos Coalition is about the last person you should look to for decision-making authority.
This should be very readily apparent to anyone looking at the organization, and yet people still gun straight for the Grand Leader, assuming that the rumors of their not being anyone important is actually a misdirect.

Awareness Unclear

It varies from person to person as to whether they're aware of the fact that they're a patsy. Some take it on as a chance to prove that they can take the heat, that they're tough enough to warrant more respect from the rest of the group. Of that lot, some even manage to thrive in the role and make the Chaos Coalition look better.
Most take it as an honor that it is not intended as.

Alternative Naming

The Obligatory Patsy