A system for positioning the eye of a patient, relative to a stationary surgical laser unit, includes a chair for moving the patient. An eye stabilizing element is held against the eye, with a tapered receptacle extending outwardly therefrom. Also, an alignment device with a tapered tip is mounted on the surgical laser unit. In operation, the patient is moved to engage the receptacle of the eye stabilizing element with the tip of the alignment device, to thereby align the patients eye with the surgical laser unit for laser surgery.