In carbon monoxide poisoning the hemoglobin is incapable of transporting oxygen to the tissues. How does oxygen get delivered to the cells when the patient is put into a hyperbaric chamber?

IT has to do with solubility of oxygen in the blood: Under pressure, much more oxygen is dissolved in the blood fluid (not attached to hemoglobin).

Because there are many more oxygen molecules present in a given volume when under pressure, hyperbaric oxygen dissolves in the blood in far greater amounts enabling it to be transported to the cells. Hyperbaric oxygen (HBO) also helps rid haemoglobin of the tenacious CO molecules, freeing it up for normal use once more. The actual amount of oxygen molecules at a pressure of 3ata (20msw) in a fixed volume is equal to 3 times the amount at the surface.