Hypnosis has had a long and controversial history in psychology, psychiatry and neurology, but the basic nature of hypnotic phenomena still remains unclear. Different theoretical approaches disagree as to whether or not hypnosis may involve an altered mental state. So far, a hypnotic state has never been convincingly demonstrated, if the criteria for the state are that it involves some objectively measurable and replicable behavioural or physiological phenomena that cannot be faked or simulated by non-hypnotized control subjects. We present a detailed case study of a highly hypnotizable subject who reliably shows a range of changes in both automatic and volitional eye movements when given a hypnotic induction. These changes correspond well with the phenomenon referred to as the "trance stare" in the hypnosis literature. Our results show that this 'trance stare' is associated with large and objective changes in the optokinetic reflex, the pupillary reflex and programming a saccade to a single target. Control subjects could not imitate these changes voluntarily. For the majority of people, hypnotic induction brings about states resembling normal focused attention or mental imagery. Our data nevertheless highlight that in some cases hypnosis may involve a special state, which qualitatively differs from the normal state of consciousness.