Abstract: A pressurized container is filled with pure oxygen. The apparatus, and the method of treatment provided thereby, are able to deliver oxygen to the blood of an enclosed premature neonate by means of directly diffusing molecular oxygen through the unusually permeable skin of such infants. Hyperbaric pressure, i.e., pressure substantially above one atmosphere absolute (ATA), preferably at least two ATA, is maintained in the container, which facilitates the transcutaneous delivery of oxygen to the blood. Means are included for protecting the eyes of the neonate and for performing physiological ventilation of the lungs thereof. The provision of normal tissue oxygen tensions facilitates the neurological development of the infant, thereby enhancing its long term quality of life.