They are, let's be honest, a slightly outlandish anachronism. A medieval remnant carrying neither salary nor authority, and with little in the way of job description beyond donning garish robes and a floppy hat to shake an endless succession of hands at graduation ceremonies.
In a world in which the vice-chancellor acts as chief executive of a corporation-like university, is there any point to the university chancellor other than keeping busy the makers of ceremonial garments?
Even those who have recently assumed the role seem rather puzzled about their purpose. In Beyond Ceremony, a 2009 report from Universities UK, Sir Menzies Campbell (chancellor of the University of St Andrews) suggested that "chancellors should be seen often, and heard rarely". Baroness Hale of Richmond (University of Bristol) was even more candid: her role as she saw it was "to be wheeled out as and when required". Lord Phillips of Sudbury (Essex) highlighted the silliness of his position: "I have to confess that, standing in my outlandish pink concoction...I often feel like a Ruritanian monarch."
At least Harold Macmillan gave those in the office a reason for being when he said: "There can't be a vice-chancellor without a chancellor."
There is certainly a whiff of anachronism among the roll call of current chancellors: the role is still predominantly filled by (usually minor) members of the Royal Family, senior religious figures and - in largest number - peers drawn from the House of Lords. Such individuals tend not to be the most dynamic and in-touch people.
But the analysis in our cover story also reveals a significant number of rather more colourful characters representing universities. About 25 per cent of chancellors are business figures, close to 20 per cent could be described as celebrities, such as Hollywood star Sir Patrick Stewart (Huddersfield), and 16 per cent are media figures, such as newscaster Sir Trevor McDonald (London South Bank).
There is a danger that some appointments can seem mere publicity stunts, but the role's nebulous nature means that it can be pretty much anything (and anyone) a university wants it to be. And that offers a real opportunity.
Put aside the pomp, forget the frou-frou and note that chancellors give their time without recompense in the service of their university, and many show real dedication. They act as ambassadors and advocates for their institutions - using their experience and networks to open doors, or using their status to help raise awareness of important challenges for the sector. If celebrity chancellors exploit their popular appeal to grab the attention of an often apathetic public, then good for them.
On graduation day, amid the ceremonial pomp, chancellors can - if they manage to avoid becoming a colourful satin-clad hand-shaking robot - help lift spirits and inspire graduates heading into an uncertain future.
Such acts reveal the essential role of chancellors: as visible and supportive friends of universities. With creativity, commitment and passion, they can play an increasingly important role as champions of the academy.
But given the difficulties facing universities, perhaps chancellors need modern garb better suited to the task. Could it be time to hang up the cap and gown of a medieval scholar and bring in the tights and cape of a superhero?