What's the cure for chronic hyperventilation syndrome?

Several things: Work with a psychotherapist on your anxiety, possibly with medications from a psychiatrist if needed for that. You have a chronic behavior pattern that requires practice to change. So in addition to the above, work with a respiratory or physical therapist on your breathing practices. A yoga teacher working with you individually might help; even learning a wind instrument. No quick fix.

Abdominal breathing.: Instructing patients to breathe abdominally, using the diaphragm more than the chest wall, often leads to improvement in subjective dyspnea and corrects many of the associated symptoms. Diaphragmatic breathing slows the respiratory rate, gives patients a distracting maneuver to perform and provides patients with a sense of self-control during episodes of hyperventilation.

Hyperventilation: We always say use a bag for rebreathing, i guess it would be funny to keep a bag over your head all the time (joke only). This is usually a form of hysterical or anxiety disorder and control of your emotions is what is necessary so you won't breath too fast. Feel yourself, if you start getting dizzy, or like floating, start controlling your breathing, start counting to 4 or 5 as you breath out.